I'm LI and the first thing you should do, if you haven't already, is have them note "Lactose Intolerant" on all of your dining reservations.
I've dined at the buffets at Boma, Crystal Palace and 1990 Park Fare. At each of these, the servers noticed that LI was noted on the reservation and they each went and got a chef to come to the table or the chef met me at the buffet line. The chefs then asked me what I couldn't have and then, dish by dish, quickly walked through the buffet line with me pointing out which dishes had dairy. Since some buffets have limited non-dairy dessert selections, they sometimes offer to bring out Rice Dream or something similar - just to tell the server.
I also dined at Chefs De France, but it was 2.5 years ago, so their procedures may have changed, but it was the one bad LI experience I've had dining at Disney World. No chef came out, the French server just said he'd note my request, but based on my reaction later the diary was not substituted. All of the dishes on the menu seemed to have dairy in them, so I had to rely on the server/chef communication. These days I'd ask to speak with the chef since that's standard procedure at all the other table service restaurants now.
I haven't been to Teppan Edo or Liberty Tree Tavern yet. But from the menu, Teppan Edo looks pretty safe except for the creamy sesame salad dressing, since Japanese cuisine rarely uses dairy. We're heading to LTT next month for lunch and I've been following the Food Photos thread and the Colony Salad (hold the cheese) looks tasty.
Dave