Granted, it's not your typical tomato-based Italian lasagna, but we thought it was quite good.
I used a bechamel sauce (that's the white sauce in the pan, which is simply equal parts butter and flour (a roux) and milk. I used 1/4 cup butter & flour and probably 1.5 or 2 cups milk. I did not measure the milk. Just slowly add enough so that the sauce is the consistency of a thick spaghetti sauce. I seasoned it with just salt and black pepper.
I put a few spoonful of the white sauce on the bottom of the lasagna dish so the noodles would not stick. Then I put down 2 noodles. I put the mashed potatoes on top of the noodles with just a bit of bechamel. Then two more noodles.
Then added the squash and half of the three medium onions I caramelized.
Add two more noodles (You will use a total of 6 noodles for a small pan like I made). If they are a little long for the pan, just fold them inside.
Pour the remainder of the onions on top of the two noodles. Top with the remaining bechamel and spread evenly. Cover with foil and bake for about 1/2 hour at 350 degrees. If you like cheese, pull it out now and throw some cheese on top. Bake just until the cheese is melted--about 20 minutes more.
Let it rest at least 10 minutes before cutting.
I can't fit any more pics on this post, so will add the finished product below.