The reason it tells you not to heat in the microwave with the lid on is because that seals it. It doesn't damage the lid itself. They ALWAYS say in the presentation that if you want to heat with the lid on to turn the lid upside down. Tomatoes/tomato sauce will stain any plastic, including Tupperware. I have some stained Tupperware to prove it, and the food was not heated in it. Not using plastic in an oven or on a hot plate is just common sense. They shouldn't even have to include that.
I have one set of the plastic L&L and never reheat any food in it. I just don't like heating food in plastic. My other set is the glass and I do reheat food in those. I prefer the glass L&L and I like that it is Bore Silica glass, something that Pyrex used to be but got away from when they cheapened their brand. Still, I wouldn't take it directly from the freezer and stick it in the oven.