Growing up cottage cheese and mozzarella was the lasagna cheeses. I don't think the stores even has ricotta cheese when I was a kid, I think the first time I actually seen ricotta for sale was when I moved away to college.
I'm pretty sure that I didn't see lasagna until I went away for college. It was not a factor in my German heritage household. The closest we got to Italian was spaghetti and meatballs or meat sauce, and even that was a rarity.
After I left home my Mom started trying some new things based on some magazines she was getting, and one of them was stuff shells. She did a really good job with them. Very tasty.
My ex really introduced me to the world of Italian food. She was Irish, but had grown up in an Irish Italian area of New York. My ex made an incredible vegetable lasagna.
Since then I've made lasagna a couple of times, but if I'm going to make something like that it's normally baked ziti. Less fussy to assemble.