When you’re planning on sending some coins and tokens, yes; your Ledger Nano S or Ledger Nano X needs to be connected to your computer or mobile phone(when using the Nano X) with an internet connection to be able to send out funds; just as you need internet connection when sending funds using a mobile wallet or a wallet installed on your computer.
No. Your Ledger Nano S/X does not need to be connected or to be online for you to receive funds. As long as you know your wallet’s address, you can freely receive funds on that wallet any time.
You do not lose your funds if your wallet is offline. This is quite a common misconception with beginners in the cryptocurrency space.