The point of Lightning is that transactions don't go on the blockchain until they need to be settled - payment channels could be open for months or years without being settled if there's no need to access the underlying currency. If everyone uses Lightning Network for the vast, vast majority of transactions (and there's no reason not to), the only times most people would ever have to put something on the blockchain is when the entity on the other end of their payment channel disappears, or they have more currency than they've ever had before.
The issue, if anything, is exactly the opposite - that there'll be little incentive to mine without enough transactions on the chain, and the security of the network will come crashing down.
Lightning Network also provides for decentralised, trustless currency exchanges - so the inflexibility of one blockchain will finally not matter much. You could pay someone in bitcoin and the other person could receive litecoin as easily as you can do similar things with a credit card today.