Depends more on the guild than on the paladin, I think. Let's give it a quick check:
SRD said:
A paladin must be of lawful good alignment and loses all class abilities if she ever willingly commits an evil act.
Shouldn't be much of a problem, there, for one who's clever. A thieves' guild that operates with order and some sort of justice would be fine.
Additionally, a paladin’s code requires that she respect legitimate authority,
Troublesome, potentially. If the Guild has at least an un-official OK to operate, he'd be acting within legitimate authority, but that would require a king with an almost Pratchett-esque touch to his rulership.

Additionally, if the guild operates in a corrupt city-state where there is no legitimate authority, the paladin is with his code, still.
act with honor (not lying, not cheating, not using poison, and so forth),
Difficult. Stealing from people kind of requires dishonorable means. Of course, it could be kind of an "above-the-board" kind of theivery? But then, in what sense would it be theivery?
Still, he could be a member in good standing of the guild without actually BEING a thief himself, I suppose. Perhaps he protects them from vigilante justice and makes sure the law doesn't come knocking at their door. He could do stuff for the thieves' guild, but I don't think he could actually steal from anyone (even someone who "could afford it" like the rich -- stealing is pretty much always dishonorable).
help those in need (provided they do not use the help for evil or chaotic ends),
Not a problem. The thieves' guild is a front for orphanages and nursing homes.
and punish those who harm or threaten innocents
Similarly not a problem. Might mean that she has to be very careful with those who are also in the guild, of course -- she can't let people skate by in the organization.
While she may adventure with characters of any good or neutral alignment, a paladin will never knowingly associate with evil characters, nor will she continue an association with someone who consistently offends her moral code. A paladin may accept only henchmen, followers, or cohorts who are lawful good.
Potentially troublesome. Thieves aren't known to adhere to a paladin's "moral code." Still possible, but they need to be careful.
...so it seems the biggest obstructions are the
act with honor and
respect legitimate authority part. A paladin could probably never rob a person. Even someone who deserved it. It's pretty obviously dishonorable. They would need to give the person a "fair chance" to hold onto their money through legal means. Which pretty much negates the thievery aspect of the guild. But the paladin could have other roles that don't involve direct theivery...a sort of "I know this happens, and it has to happen for the greater good, but I can't do it myself." That could get sticky with the bit about associating with those that offend their moral code: if they know people in the guild that do this, it's pretty offensive to the moral code. At the same time, they HAVE to know, because they can't choose willful ignorance as an excuse to let evil flourish (which would hurt their Good alignment standing).
...so I'm not entirely sure they CAN. Thievery is dishonorable (even when it's Lawful Good). Any position would force the paladin to at least turn a blind eye toward dishonorable behavior, something they really can't do.
I think this would be a good Lawful Good vs. Lawful Good conflict. Both the guild and the Paladin believe that they are achieving the most good for the most people, but the paladin cannot abide the existence of the guild, and as long as the paladin is trying to thwart them, the guild can't rest easily.
Yeah, I think that's a "no." And I'm kind of surprised at that, since I'm very sympathetic to lawful revolutions and the like. The more specific code of the paladin gets in the way, here.