What would happen if all Bitcoin is mined and all Bitcoin is lost?
Lost means that if it can't recover then it will definitely become worthless. And if Bitcoin starts to constantly disappear from the total supply then of course Bitcoin will slowly increase in demand and the price will likely increase a lot.
If there is no Bitcoin left to use then there will be no market for it. It is simple that when there is no supply no matter how huge the demand is, the market will die.
However, since Bitcoin is decentralized and there is no way to increase the supply like paper money, the more Bitcoins are lost from the supply, the more pressure there is on the amount of Bitcoins left.
Bitcoin developers can alter the total number of Bitcoins if they want to but due to the consensus system, this kind of action may probably not materialize unless they all agree to change the number of total coins which can possibly result in a hard fork. Remember Bitcoin is only a program that can be altered anytime the only problem is the implementation since it has to pass through the consensus system.