No, you only pay a fee when opening and closing a payment channel. Once the channel is open, you can transact freely (i.e. as many times as you want) with the other person in the channel at no cost. If you want to transact with someone outside of the channel but there is some route to them through LN channels, then you can use your same channel to pay that other person by routing a payment through other channels. This routing of payments will either be extremely cheap or have no cost, depending on whether node operators in the route charge a fee for being routed through.

If you are just going to make a single transaction with someone and you don't plan on using them to route payments to other people, then you should not create a channel for that. Just make a normal Bitcoin transaction.