This sort of scheme is common so that you do not have to share the encryption key with the provider. You derive two keys from your plaintext password: one used for authentication and one used for encrypting / decrypting the blob. This way, Lastpass can authenticate you without having to see the key to decrypt your data.

Not sure the specifics of how lastpass implements this but this is a really common approach for end-to-end encrypted apps.

The client-side hashing is actually the part that keeps your master password a secret, from everyone including LastPass yourself. This makes sure that LastPass cannot decrypt your passwords despite them being stored there. The server-side part on the other hand is severely misimplemented and not much good to anyone. This is one of the issues I’ve written about here: https://palant.info/2018/07/09/is-your-lastpass-data-really-...

From what I understand: you still need the master password locally to decrypt the individual passwords. A hash won't provide that. All you're doing here is logging into LastPass.

Hashing client side has a non-cryptographic benefit of making all passwords a fixed length. This, in turn, helps avoid accidents with bcrypt misuse.