I'm surprised that LastPass's policies aren't at least that strict.
My company has what I think is a big hole in this policy in that we're allowed to use our own phone for email, a few corporate apps (like Jira) and our corporate password manager (not LastPass), but IT doesn't do any management of phones (other than being able to wipe them remotely if you're connected to the company email server). I suspect that the company doesn't want to spend the money on giving everyone a managed phone.