My DS is the same as yours - now he is 3. I have given him traditional type meals from young, like roast/fried chicken/lamb/fish with potato/rice/pasta and veg. That is what he eats for his main meals now, I just vary the foods. DS has quite a lot of ketchup with this, otherwise gravies.
Lamb is good to give as it contains lots of nutrients, is good for people with allergies and contains high fat which is good to make up for not drining full fat milks.
for snacks,you can try toast/rice cakes and jam, fruit purees. chocolate bourbon biscuits and hobnobs have no dairy or egg, nor do most own brand rich tea type biscuits but you need to check the labels.
I get a yeast flake food supplement which tastes nice and DS uses this instead of grated cheese to sprinkle on top of pasta sauces. I use breadcrumbs instead of cheese for toppings on shepherds pie etc.
Tend to hardly cook cheese/white sauce type dishes though.
Eating out is a pain, so we go to mcdonalds cos you can be sure of the ingredients or alwyas take some sandwiches for DS when we are out.
Anyway hope this can be of some help. I found it hard at first but am used to it now, but can be a pain at times, especially when out.