I forget if LastPass does — 1Password does (though I haven't actually used it in practice, because my work doesn't use 1Password). Idk, maybe it's not actually a problem, but it's how I like to organize things. ::shrug::

Lastpass allows you to link your personal-personal account into your work account, so that you can access your personal-personal data while logged into a work account. Work-personal accounts should be stored in a personal folder in your work account, then work-work accounts are in shared folders that cross multiple users.