Yes. The compensation for the miners comes in the fees within the blocks. I'm assuming that the volume of transactions by then or the derived fee as a result of off-chain transactions would be sufficient to compensate for it.

It is highly unlikely that Bitcoin would insecure by then. The way the block rewards are reduced gradually pads any impact on the miner's income and we're most likely going to see the impact far sooner than the 2140 timeline.