On The Lowdown, the action picks up where it left off last week, and characters drift in and out of Lee’s story, freed from the burden of an arc. The looseness (so far) works for me, because Lee Raybon’s fast days don’t end. His misadventures crash into one another. His problems accumulate. His arc is crescendoing chaos.

The looseness also mirrors something rare and powerful about Lee himself: how he authors his own fate, sets his own hectic pace, never checks a calendar. He’s a shop owner who never sells, a writer who never sits at a desk. In “Dinosaur Memories,” Lee is abducted — improbably but not unbelievably — for the second time in three episodes. This man is not a wealthy heiress or a foreign spy or the key witness in a RICO case, so how does it already seem so plausible that Lee would be abducted twice in quick succession? The series is a character study masquerading as a murder mystery.

And only when the series reminds us that it’s a murder mystery does it lose speed. The Washbergs, Blackie and Berta, and Allen the ginger skinhead — right now, the who-, why-, and howdunits feel tacked on, excuses to watch Lee unravel, rather than the cause of his unraveling. Isn’t Lee the kind of guy who’s always chasing something down or fucking things up, talking his way in or figuring a way out? He exists in a state of perpetual unraveling, afraid of what he might find out about himself if he ever makes it to the far end of the thread.

It’s Lee’s weekend again, which means Frances has been signed up for another marathon. They start by checking out their new apartment on the rough side of town, which, for the teenage daughter, includes the ickiness of listening to someone hit on her dad. It’s Vicky, the same unhinged Realtor who managed Dale’s estate sale. In between barely veiled come-ons and apartment specs, she divulges that Ray never picked up those Jim Thompson first editions Lee had paid him to buy from Dale’s collection.

Whatever Lee was planning to do next is a memory, not that I believe he makes plans. Instead, he ricochets — from the apartment (excuse me, “quadraplex”) over to the antiques mall, where he confronts Ray about the missing books. Ray confesses that Catalina Estragon, the antiquarian bruja from Keystone Lake, beat him to the sale, and he thinks it’s unlikely she’ll give up the books because she’s a coldhearted sorceress who drinks men’s blood. That said, Ray bitches so indiscriminately about every single person in Tulsa that he’s hard to trust.

But Lee seems to like him. Maybe because Lee’s similarly allergic to quiet, he understands that just because a man is talking doesn’t mean you’re supposed to listen. Some people have a personal word quota they’re programmed to hit each day, no matter what. Why else would Lee tell someone as shifty as Ray so much about what’s going on? Ray doesn’t need to know that it’s what’s inside the Thompson books that’s important to catching Dale’s killer, if he was indeed killed. Ray doesn’t need to know that Akron Frank and Donald Washberg are somehow connected.

Lee corrals Ray into his van along with Frances for the drive to Catalina’s houseboat, which she shares with her poacher husband. When they get there, Lee assigns tasks. Frances’s is to wait at the marina restaurant, and Ray’s is to babysit Frances. Meanwhile, Lee “borrows” a U.S. Department of the Interior jacket off a federal agent sitting at the bar and boldly boards Catalina’s boat, the Disturbing the Peace.

His plan is to pose as a Fish & Wildlife agent, there to question Catalina’s husband about poaching … and then what? Take off with a cardboard box of first editions and make a getaway? It doesn’t get that far. Instead of books, Lee finds evidence of a counterfeit-caviar operation. Before he can locate Catalina, he is bludgeoned with a shovel. There’s such incessant action on The Lowdown that it’s a miracle the show remembers to be funny. When the angler-cum-soldato who catches Lee snooping eventually delivers him to the big boss, Marlon, he proudly declares, “Got him with his dick in the cookie jar.”

Marlon is a bad guy. His knuckles are as bloody as his face, and he can tell instantly that Lee is no field agent; the man’s wearing bootleg jeans. Having accidentally stumbled upon a criminal fishing outfit — these guys are peddling paddlefish roe under the label of beluga caviar — he now knows too much. A missing Fed would bring a lot of unwanted attention to their lake, but a missing Tulsa man in Saturday Night Fever flares? Is anyone even going to notice he’s gone?

Mercifully, Marlon gives Lee a chance to prove he can be trusted. “Tell me your tale of woe,” he offers, right after force-feeding Lee unprocessed paddlefish eggs straight from the fish’s swollen ovaries. It’s pretty gross. So Lee tells the story he has been on the cusp of telling all episode long, ever since Ray, in one of his mile-a-minute monologues, let slip to Frances that her dad is an ex-con. At the time, Lee minimizes the bombshell by way of embellishment. He may technically be an ex-con, Franny, but so were some of the world’s best men — Nelson Mandela, Oscar Wilde, Merle Haggard.

What actually happened, Lee tells Marlon, is that he was heading to Dairy Queen when a buxom woman offered him methamphetamines and then disappeared, leaving Lee naked in someone else’s car with a three-legged dog and a guy called Juan hog-tied in the back seat. The cops showed up and arrested him for God knows what, but Lee definitely didn’t serve four days and one morning for protesting apartheid or being gay in Victorian England. As his story comes to a close, Lee starts crying, worried that he let down Frances the day of his arrest and that he’s letting her down right now, which he certainly is. Her babysitter is on his third or fourth double whiskey.

Marlon deems Lee reliable. The story has too many rich details to be a lie, and Marlon knows something of woe too. When Lee mentions he was actually aboard the Disturbing the Peace to find Catalina and not to vanquish poachers, it comes out that Marlon is her long-suffering husband. He loves Catalina but struggles to tell her. So Lee and Marlon strike a deal — Lee’s freedom in exchange for his pen. On Marlon’s behalf, he writes an ode to Catalina, which doubles as Lee’s vow to Frances: “I would do everything that is within me to give you the life you deserve.”

Frances is a good girl. She sits with Ray through a few rounds, sincerely empathizing as he tells her about coming out to his Bible-thumping mother at 15. But she’s also her father’s daughter. Anxious that he hasn’t returned, she sneaks out of the restaurant to look for him on Catalina’s boat. Like Lee, she’s self-sure and determined; when Catalina discovers her sniffing around, Frances has a good sense for when to lie and when to tell the truth. For her part, Catalina doesn’t seem like the bruja we were promised. Instead of kicking Frances off her boat, they chitchat over maté.

One truth Frances offers is that even though he left her alone all day, Lee’s a good father. Catalina, of course, sees only a naïve girl desperate to love the ne’er-do-well she’s stuck calling Dad. When Catalina goes into the kitchen to refill her calabash, Frances grabs the box of Thompson paperbacks and makes a run for Ray at the restaurant. Catalina catches them. The geography of this tiny marina — one restaurant, a big parking lot, and a few boats — makes it impossible that she wouldn’t. For reasons unknown, Catalina responds to the attempted theft by burning the books, which is the only indication that she might be a witch. Fire is kind of witchy.

Luckily, clever Frances must have understood her caper was destined for failure. Before she brought the books to Ray, or maybe when Ray was slowly paying his bar tab, she leafed through them for what was inside. This is the best outcome for Lee, really. He has Dale’s letters in hand, and anyone who might ever get the notion there were letters to begin with will think they’re ash.

Not much else happens to the others in “Dinosaur Memories.” Waylon and Henry hang out at the bookstore waiting to become YouTube celebs. Marty has a series of bad encounters. First, Donald asks his old pal Chubs to get rid of his mistress, Betty Jo; in exchange, Marty can head up Donald’s gubernatorial security detail. But Betty Jo makes it clear to Marty that she’s not going to disappear for a measly $10K. If the Washberg trust wants to evict her from Dale’s ranch on the basis of a decades old prenup, they should expect war.

Then there’s Marty’s not so coincidental coffee-shop run-in with Allen. We learn this week that, on top of being a racist and a murderer, Allen’s an ageist little snot. At first, he praises Marty for dealing with the disturbance Lee made at Dale’s memorial, but really he’s there to spook him. He knows Marty has been tailing Lee, and because Lee talks more than he does, Allen knows Lee told Don he’d been abducted by skinheads. Does Allen know that Lee saw him kill Blackie and Berta? He must at least suspect it.

For now, though, Lee is safely reunited with his daughter, who is also his partner in crime. In fact, a hilarious if idiotic Scooby gang seems to be forming to solve “The Case of Black-Sheep Brother.” There’s Lee, a citizen journo with delusions of grandeur; his daughter, a gumshoe and a daddy’s girl; and the ghost of Dale Washberg, who can be summoned by reading the notes he left tucked into his crime novels. Frances can see him, too.

I believe in this ragtag group. I think they’ll find Dale’s killer. I can already hear Don — or Betty Jo? — grumbling about it in a few episodes’ time, as he’s being walked offscreen in handcuffs: And I would have gotten away with it, too, if it weren’t for you bookish losers.

 Frances is a good girl, but she’s also her father’s daughter.