I support this feature request. I'd recommend checking both usernames/emails and passwords since the API allows for checking both. I sometimes append a unique identifier to my email, so it'd be hard to check all those too. With each site having a unique password it would take a ton of time to manually check each password, one by one, on the HIBP website.
It'd be nice if LastPass notified us of breached usernames/emails and passwords in our account. I realize, because LastPass doesn't have access to those, that it'd be impossible to push a notification automatically, but it would be cool if it checked all credentials upon login (or at login after a specified interval of time). But even just building it into the Security Challenge tool would work (LastPass reps have stated in the past that they're already doing this with another service, perhaps they can add HIBP though).
Thanks for all your work LastPass! Hopefully this can be added as well. I think we'd all feel more comfortable knowing our data has been checked against breaches and being notified so we can take action!