The LotFP "Specialist" system is appealing to me because of its flexibility (each thief can specialize in specific skills rather than advancing slowly in all at once) and because of its simplicity. There's something appealing about rolling the single d6 rather than percentile dice. LotFP handles non-thief classes trying to do thief stuff by saying that all non-thief classes have a flat 1/6 chance of success. Which is nice and simple, but maybe a little restrictive.
Here's my spin on it:
When a character of any class attempts to do something thief-y, they get a flat x/6 chance and also an attribute check at a high difficulty. They only need to make one of the two rolls to succeed.
I do attributes with the xd6 roll under method, rather than a straight d20 roll, because it makes it so easy to modify the difficult of check. I would decide whether the check was 3d6 roll (for something that an average non-specialized character could have a good chance of succeeding on) 4d6, 5d6 or 6d6 for something that only a specialist should really be able to handle.
For example, Marsters the Magic-User is attempting to pick a lock of average difficulty, and has access to some small tools to do it with. I'd probably rule that he would make the dexterity check with 4d6, since it's kind of a skilled job, but one that he has the tools for. Since Marsters has a dexterity of 9, he has to roll equal to or under a 9 on 4d6, or a 1 on a d6. If he succeeds in either roll, he's picked the lock.
I'm terrible at estimating percentages from dice rolls, so I'd need to keep an eye on how difficult these rolls end up being in play. If it turns out that the thief is getting outperformed by other classes, I'd probably just increase the dice used in the attribute check.
Thief/Adventuring Skills and related attribute check:
Pick Locks/Tinker: Dex
Pick Pockets/Sleight of Hand: Dex
Sneak Attack/Backstab: Dex