My daughter has vegetarian friends who eat dairy products so when they visit I often make two lasagnes, one meat and one vegetarian. I'd be happy with just the vegetarian but the rest of the family prefers the meat one.
I make a sauce as I'd make normal bolognese sauce, but instead of meat I put in heaps of small-diced vegetables- green peppers, zucchinis, celery, mushrooms, leeks, and grated carrots. Simmer until it's like bolognese sauce. Then layer as usual with pasta sheets and I use a bechamel sauce with heaps of grated cheese melted through. I know some vegetarians use ricotta cheese instead but ricotta requires a 50 mile round trip here and I don't usually get that much time to plan ahead :-)
Hope this helps
CJ