Offline access is dependent on login type
If Your Vault is Protected with Master Password Login
Yes, you can enable offline access by following the instructions on LogMeIn's support page.
Please Note: For offline access, your stored passwords must not be hidden from view in your LastPass Vault.
If Your Vault is Protected with NetID Login
No, however, LastPass (LogMeIn) is currently scoping this functionality. To mitigate any concerns, NetID Login is a reliable service and LastPass Enterprise sessions will remain active for 14 days (unless you manually log out sooner).