My understanding is that you start by doing an actual BTC transaction of, say X USD, for which you pay the fee, and then you can "spend" up to X-fee USD in the lightning network. People who receive payment from you can opt for getting a BTC transaction from your stash or use it to do other payments.

The base idea is that it uses the BTC network as a dispute settlement fallback. "It works but is expensive, let's just exchange through the lightning network".

You can see Lightning as being a network that exchanges "BTC IOU". If the network decides for some reasons to be hostile to you and refuses to broadcast the transactions where you receive money, you still have a signed token that proves you have the BTC IOU and that are acceptable by the BTC network (for the cost of a fee)