Only if you give your keys also to that web service.  In other words, your bank.  You have to stay online to be able to sign at any moment with your own keys.  If you want another service to do so while you are offline, you have to give them your keys.  But then, they have your coins.  Like an exchange, or a bank.

In fact, the only safe way is to have the server hardware in your own place (say, an old PC running in your basement).  Even using a VPS service on which you run your own LN wallet is not safe, because of course the administrator can access the keys of the wallet if it has to run.  You cannot keep them encrypted, because the wallet software needs to access them all the time.  So the only safe way to run an LN wallet, is to run it on a clean machine over which you have physical control.  In exactly the same way as you do bitcoin transactions right now.