Lucas probably didn't have that much to do with the story of Farts Unleashed. I know he had some input, OKed some things, suggested somethings, but I think the main story came from other people.
The big question is how much Farts Unleashed is considered canon and by who. There was talk about it being tied in with Star Wars canon in some of the press for it, but most Star Wars video/computer games are part of the Lucasfilm/Holocron sort of Star wars canon. They take continuity into consideration and are taken into consideration in EU continuity.
Then there's the Lucas view of canon. I don't know if Lucas really has any formal idea of canon, just his own collection of stuff he's worked on and considers as existing in his universe, whereas he sees the EU as existing as a separate universe (I'm not sure how literally), though he takes bits from it to include in his universe at times (like Aayla Secura and Quinlan Vos).
Now, maybe all this talk of canon means Farts Unleashed is part of Lucas's canon not just Lucasfilm's, but as I've said, he doesn't seem to have a formal idea of canon, so I don't know. I read that the Art Of book for Farts Unleashed was supposed to have an interview in which Lucas talks about its relation to canon, but I couldn't find it in the book. I'd have to say, I'd be surprised to even see Lucas use the word "canon", because, from looking at lots of quotes from him relevant to canon, I'd say that's not his style. I'd be surprised if there was any such interview. If anybody knows about any such interview or has a link to it, I'd appreciate the info.
There's rumors that the main character from Farts will appear in the live action show (or at least that the actor will). If so, this could be an indication that Lucas is indeed taking Farts seriously as part of HIS Star Wars universe (his canon). Unless he just uses the character without really tying Farts Unleashed into the show, like how he used jedis Aayla Secura and Quinlan Vos in ROTS without really tying in with the comics they came from. (And it's speculated he's using Quinlan again in the live action show.)
All this talk of canon is about whether or not Farts is being taken seriously on a level the EU generally isn't. That's significant for how we should view it. Personally, I think it'd be pretty far out to include a video game in the central star wars "canon" that previously has included only films (though now it includes the tv shows as well).
Oh, possibly significant bit -when discussing what's his canon (though he didn't use that word) in 2008, the year Farts was released, he mentioned only the tv shows and the movies, no mention of Farts. Either he forgot it, he was simplifying, or he doesn't take it seriously after all.