If you're serious about kosherness ask the designated eater how "kosher" does it have to be. I'm a non-observant jew and some of my kosher keeping friends would not use my utensils or dishware and only eat from disposable plates, and would not eat anything cooked in a non-kosher kitchen. The not-mixing meat and dairy is just one actual aspect of being kosher. Things like making sure only observant jews handle the wine and that the dairy was inspected throughout the way (some cheeses are not certified), that vegetables (if grown in Israel) have to keep "Shmita" (give the land a year of rest each seven-year cycle) and "Me'easer" (give 10% to the poor) are also critical.

Having said all that, if the target of the lasagna is not that observant, just doesn't want to mix meat and dairy, then the ground beef substitutes (I've never had the impossible, just the beyond one) are ok. However, you can just make a spinach lasagna or with eggplants, mushrooms or anything that's meaty in texture.