Lastpass (like pretty much all of these online password managers) will work offline, so if the service goes down, you can still access your data locally.
Google(Drive) at least I trust to have the engineering resources to keep data secure, perhaps not from government secret services but at least random hackers
You do need to trust them enough that they will never sniff your master password (AFAIK even the web vault is local only) but eg. the command-line client is open source, so you can at least verify their protocol.
That said, I might switch to bitwarden at some point purely because it can be self-hosted.
All the downsides of online services are mitigated by:
1) Keeping a local backup of your passwords 2) Using a service which only stores encrypted vaults which are decrypted on your device with a locally stored password.