Since I recreated the outdoor survival maps in CC3+, I haven't actually used them myself yet. I haven't really been gaming at all unfortunately. But I have been slowly working on a system to combine the OD&D 3lbbs and Chainmail.
While doing this, I've been thinking about including the thief class. While I know the thief isn't traditional in a 3lbb only game, I feel it is a stronger fantasy archetype than the cleric is. So as I start working out this system for my future OD&D & Chainmail West Marches style game, and a solo game for my wife, I've been analyzing how others have treated the thief in this context.
I've looked at a set of notes of how Gary Gygax apparently thought about including the thief before Greyhawk (I honestly have no idea how dubious this claim is), as well as the following these other resources/clones:
Edit: I want to note there is a flaw in my method. In the systems I analyzed, I did not check them against OD&D itself, but how they relate to the other classes in their own system. I might go back and practice this same exercise but see how it stacks against the lbbs.
Note on my shorthand: NA means the information wasn't applicable. Typically this refers to the fact that they completely scraped the Fighting Capability chart. Sometimes it was that they had just copied the d4 HD from greyhawk. AC means Alternate Combat. Since most did not have a recreating of Fighting Capability, I instead compared how they leveled in the Alternative Combat system.
I've been surprised by some of the results. I understand the thief gaining HD similarly to a Magic-User, or a cleric, but some documents make them gain HD slower than Magic-Users? Sometimes their Fighting Capability is even worse than a Magic-User in Delving Deeper v5
Thieves skills ran the gamut from being essentially worthless at early levels (like D&D is traditionally), to having a decent chance at success.
There really was not much difference in how backstabs were handled. +4 to hit with double damage, and it increasing to triple and quadruple at certain levels was pretty standard. Spellcraft & Swordplay was only a bit different since it is a 2d6 system.
Now I'm trying to think of how I want to handle the thief. I plan to take the XP chart from Greyhawk. I think I will go with a HD that either matches the Magic-User, or is somewhere between that and the Cleric. I think I'd give the Thief a Fighting Capability either matching the Cleric, or in between the Cleric and MU. For Thieves skills, since I am planning on Chainmail and stuff, I think I'd prefer one of the d6 systems. Either ripping from Lamentations of the Flame Princess (which is what I've done in the past) or taking one of the 1d6 or 2d6 systems shown above. I prefer for the thief to be somewhat competent at early levels. They're already not great at combat, so I would rather them not die constantly because they're tasked to disarm traps with their minuscule chance to do so. For backstab, I think I'd have to go with something a bit different than what is shown since I'm thinking about troop and man-to-man combat. +4 is what too large of a bonus. Maybe an extra die on an attack in troop combat, gaining more than just 1 extra die as you level, and maybe the +2 or +3 for Man-to-Man.