The computation does not change, only the reward. That is the beauty of it. The speculation is by that point transaction fees will be high. The dream state would be for everyone to be on LN and I am guessing on-chain mempool would be mostly saturated with LN channel related transactions.

What miners do would still be important and critical to network security because they are ensuring you cannot brute force the next block. This guy has a great video on it: https://www.youtube.com/watch?v=vdaD-HJLycM