LML has worked fine for some time now, but as of 2022-01-05, I can confirm LST to be working on Linux.
One thing that I noticed, there are no beeps when the game boots, but everything else seems to work fine.
TL/DR: Install the mods like you would usually, then copy my launch command.
System: Arch Linux x64; Kernel: 6.1.2-arch1-1 (latest); up to date as of 2022-01-05
RDR2 Version: Steam
ASI Loader: LMS
Tested Mods: Navy Revolver (SP), Red Dead Offline
Proton Version: Proton 7.0 for setup (creation of prefix, install of Rockstar launcher, first game boot), then switched to GE-Proton7-43
Changes to the prefix by user: none
Launch Command: (This includes AB's Scripthook, LMS's ASI Loader, LML and LST)
WINEDLLOVERRIDES=EasyHook,EasyHook64,EasyLoad64,NativeInterop,version,dinput8,ScriptHookRDR2,ModManager.Core,ModManager.NativeInterop,NLog=n,b %command%
My actual launch command with all the bells and whistles (MangoHud, Gamemode, maximum placebo or something like that (meaning everything after "%command%"):
MANGOHUD=1 WINEDLLOVERRIDES=EasyHook,EasyHook64,EasyLoad64,NativeInterop,version,dinput8,ScriptHookRDR2,ModManager.Core,ModManager.NativeInterop,NLog=n,b gamemoderun %command% -USEALLAVAILABLECORES -cpuLoadRebalancing -ignorepipelinecache