Make the sauce first. Drain the tomatoes (reserve the juice) and put them into a food processor; chop to a rough puree. (You can also do this with your fingers in a bowl.)
Heat the olive oil in a saucepan over medium heat till the oil shimmers. Saute the garlic and crushed red pepper for about a minute--until you can smell the garlic.
Add the tomatoes, 1/2 cup of the reserved juice, basil, oregano, and salt. Bring to a boil, and lower the heat to medium-low. Simmer for about twenty minutes, uncovered. Then keep on the lowest possible heat while you continue with the rest of the recipe.
Bring a large pot of water to a boil with 1 Tbs. salt and 1 Tbs. olive oil. Add the lasagna noodles and boil for about two minutes, or until the noodles are no longer stiff. Remove to a bowl of cold water for a moment, then remove and drain. (Leave this step out if using fresh pasta sheets.)
Cook the spinach in the same water you used to cook the pasta, just for a minute. Remove with a slotted spoon, drain, and spread out.
Cover the casserole with aluminum foil and bake in the center of the oven at 350 degrees for 40 minutes. Remove the foil and return to the oven until a light crust has formed on the top.
After removing from the oven, let the lasagna rest for at least 15 minutes before attempting to slice. Serve with a wide metal spatula to keep it together (almost impossible to do with the first slice).