So I need to send some btc to a wallet that has a receiving capacity on its lightning network channel?
Yes. By they way, if you don't want to worry about incoming capacity and your node's connectivity then
BlueWallet might a good choice. It is a custodial Lightning wallet which is fairly easy to use. A third-party handles the most difficult parts of using the Lightning Network.
Is there a sevice that provide this kind of thing?
There are some services which will accept your Lightning payment and send you an on-chain payment for a small fee and vice-versa. The only such service I can recall is
Lightning Conductor. You could also send some of your funds to an exchange which supports deposits over the Lightning Network.