Gluten free and even dairy free doesn't mean a lasagna free life.
Gluten free lasagna noodles, dried and in boxes, exist and won't leave you sad. Although please do not believe the 'no pre cooking' hype. They do not need to be fully cooked before using but they do need some pre cooking to avoid being icky.
If you use box pasta then you are set to follow any recipe from any cookbook for lasagna.
In its simplest form lasagna is layer of sauce, layer of noodles, layer of cheese and repeat; bake at 350 degree until browned and bubbly.
If you are skipping box noodles then you have some choices to make - fresh pasta made by you or veggie 'noodles'.
Veggie noodles are merely very, very thin sliced squash (zucchini and butternut are my top choices). Then use those strips in you favorite recipe.
As for dairy free - I find the soy cheeses do better than the nut cheeses but they do a bit better than than the rice cheeses. (see my cookbook for more substitutions)
Making fresh lasagna noodles isn't too scary either. Actually I find it easier than trying to slice thin squash without a mandoline. Fresh pasta is basically flour, egg, and water. Instead of semolina and durum wheat I use potato and sweet rice. The rest is the same - flour, egg, water, (but roll out between plastic wrap to avoid a too sticky situation). A bonus with fresh is you don't have to pre cook; just let the pasta dry out on until it is no longer tacky then slice.
Now you are ready for Garfield as a dinner guest.