No, you don't have to swap your bitcoins. The Lightning Network doesn't use any form of tokens; it uses real bitcoins. In order to be able to transact using the Lightning Network, you have to open a channel using a wallet which supports the Lightning Network (i.e. Zap, Eclair Mobile). When you open a channel, you lock up your coins in a multi-signature address which is controlled by you and the other node. Once you have opened your channel, you can send payments over the LN (with some limitations). Every time you send a payment over the LN, the balance of the channel updates but it's not broadcast to the Bitcoin network in order to save money on the fees. If you want to retrieve your coins on-chain then you have to close the channel. The amount of coins + routing fees you spent on the LN will go to the other node's address while the rest minus the closing fee will be returned to you.

It's a little bit more complicated than that; consider reading basics of the Lightning Network and The Lightning Network FAQ if you want to learn more. It's not a perfect solution. Keep in mind that some of your payments might fail and not many merchants accept LN payments.