Actually, you hit well upon why I don't like rolling dice in a box lid...the cardboard does have that very effect...the dice "slide" rather than roll correctly, and the cardboard "cushioning" or "flimsiness" (whatever you want to call it) also cause the dice to not bounces and tumble well.
For those who don't like dice towers, that's the beauty of a dice tray: they are generally felt lined, but the undersupport is that much like a cassino table; and the sides are wooden. Most dice trays are octagonal in shape, but come in other shapes as well, all of which also keep the dice moving, as they can often hit two sides and "spin" the dice as they tumble. And their not usually very big and cumbersome...I think they come anywhere from 8"-16".
Dice towers make a lot of sense to me. They supposedly go back as far as Roman times...I can't verify that, but I wouldn't dispute it! The problem being, build your own or buy it pre-made. There are actually many styles out there...the one I've seen the most is the plexiglass on, which I think adds to the enjoyment of seeing them bones spin and tumble! But, they are a bit loud, and I imagine it can get grating on the nerves in a long game, no? One of my favorites that I've seen is designed to look like a Big Red 1's Infantryman's locker! Too cool!
Whatever your preference, keep throwin' them bones!