I have seen this before in many websites. They recommended not only for Lightning network but also for storing a private keys for Nostr. I think I will try this one first. Many thanks for letting me know!
Discussion
No you dont store your private key!
There is two key on nostr
Npub & nsec.
Npub is a public address. When you register your npub on getalby, you kinda get a username
See mine : ihsanmd@getalby.com
When you activate the LN wallet on getalby.com
You get a custodian LN wallet with ihsanmd@getalby.com as the LN address
You should never gives your nsec (private key) at all cost to anyone.