if the bitcoin lightning network has been successful the costs or fees will no longer exist.
It depends. If you directly transact with the party you have an open channel with, transactions are practically free. If you however hop your transaction through multiple nodes, fees may still apply. The only difference is that the lightning fees are waaaay lower than on-chain fees, so even if you end up paying a fee, it will be 10-100 times less than what you pay on-chain. Maybe even lower if the market effect kicks in, because you can ignore certain 'expensive' nodes to find a cheaper route.
In lther altcoins there are already some of it that has no fees you just have to know what are these coins and if they will last until in the future.
Altcoins with no fees = altcoins with no network activity.