I have found that I can use Mizithra in almost any recipe where Parmesan is included as an ingredient. As cayjohan's comments indicate, it is an excellent addition to salads, meat dishes and (of course) pasta dishes. My wife enjoys it as a topping for soups and stews too. I use it in Ravioli and I sprinkle it over Ravioli with red sauce.
Cat Cora has a recipe using it with lamb:
that I like very much.
Our table seems to like it shaved onto a fairly citrus-y salad (lemon juice for the dressing acid, or maybe slices of orange with the greens). We almost always add some oregano, as it seems to marry well.
Also, try making some lamb meatballs/patties. Grate some myzithra into the mix. Very nice.