LastPass is already doing a great job in generating unique passwords to avoid that compromised passwords are also allowing access to other sites as well.
The same issue also holds true for potentially compromised email-addresses that have been used for logins for different services.
If LastPass would offer a service that allows to dynamically generate email-addresses that can be used as logins would create an additional security layer in case a service has been hacked and user data have been compromised.
This generated email-address needs to act as an email alias to the actual email address of the LastPass account to allow verify-email-adresses to come through.
DuckDuckGo just added a similar service (see https://spreadprivacy.com/introducing-email-protection-beta/) but i think it would be an even better addition with the password generation capabilities of LastPass.