if you use an LSP (lightning service provider) then those have a fee. e.g. @LN⚡Server

Opening a lightning channel is just a normal bitcoin transaction. So the fee goes to the miner who mines the block, same as with every other on-chain transaction. If you buy an incoming channel from an LSP, then they charge a fee that is usually a bit higher than the pure tx fee. But if you spend through your own channels first, you can create incoming liquidity for free (i.e. the overall amount you spend).