Henry X has fed factory and reloaded 38 for me w/ no issues.

With levers, it's more of the bullet profile.  For cowboy shooting, I always used truncated rounds.  A better profile than round nosed flat points.

ETA, mine is a Cimeron trapper.  10 38s or 9 .357 with my loads, in the tube.

Not sure if it can be threaded.

I have the 1894CST, 1894 Dark, Henry Big Boy X, and Rossi Triple Black. They all feed 38 special fine except the 1894 dark which would hang up occasionally before I sent it out for an action tune up. The Rossi triple black was actually great shooting and handling but I sent it back for warranty on account of a canted rail.  Like mounting a red dot would be leaning left at 11 oclock which bothers me.  The mag tube also extended ever so slightly past the barrels shoulder - I use 3-lug but made it a no go on any other mounting method.  They are now sending me a replacement firearm; I really liked the rifle so hoping the replacement is squared away.

Of all those I think only the Henry and Rossi regularly come in stock as of fall 2021.  I would only choose a Rossi as long as you are able to inspect. It is much lighter feeling and handier than the Henry but good luck on the QC. I also wouldn’t rule out the Ruger 77/357 as a bolt gun alternative. Pretty fun one too.

My R92 (Rossi Triple Black) likes any round profiled 38 bullets just fine. (Or anything loaded long.) It does not like wad cutters. I love the carbine.

My 357 X feeds PCCB wadcutters no problem. Maybe even a little better than the 77/357

My Rossi 92 feeds 125gr FRN in 38s with no issue.

OP, I've been pretty lucky with Rossi R92s and Marlin 1894s feeding both. I don't think it's a "best model lever gun for 38 sp" it's more of a individual gun thing..

Since you reload, I wouldn't really worry about it. My first .357 lever gun cycled 38sp but didn't like the OAL of the .357.   Things came together and it likes both. 4 x 38/357 lever guns later and not one of them has a problem with both..

I have a Rossi .357 but not one with a threaded barrel and it functions perfectly with fmj but not lead/soft points, as it hangs up on the ramp. I thought about taking it apart and polishing it but I don't have many soft point/lead ammo left.

My citadel levtac 357 has had no issues feeding all the 38 spl I want to shoot.