Practice, baby, practice.
Man, that joke never gets old.
If it's at a time when the Animal Kingdom Theme Park is still open, your best bet would be to take a bus to the park, then transfer on a bus to the Lodge. Since the Lodge is so close to the park, there's usually more buses going to and from there than most other resorts.
However, if the park is closed by then, I think anything will be a crap shoot. Take the first bus you can to any of the other 3 parks, then transfer from there to AKL. I'd probably avoid taking a bus to Downtown Disney, only because you'll be going all the way over to the east side of Disney, then all the way back over to the west side, where AKL is. The odds of it taking more time is much greater, since you're going completely the opposite way first. However, if all the parks are closed by the time your meal is done, then you may have to return to your resort via DTD anyway.
You may want to consider biting the bullet this once and hiring a cab.