What is important that there is a transaction confirmation in Ledger Live, so you send it to correct address and it is in your wallet. Sometimes Ledger Live is have problem with displaying the incorrect balance, and this can be related to application cache. In order to fix that you need to clear cache and resync for data by doing this steps in Ledger Live :

-Click on Settings.
-Click the Help tab.
-Click the Clear button to clear the cache.
-Click Confirm after reading the instructions. The application will then reopen to your dashboard.
-Once Ledger Live is synchronized, your balance should be correct.

More info : https://support.ledger.com/hc/en-us/articles/360007412333-Fix-an-incorrect-balance