

Human: Should I browse someones phone if they lost it to try to contact them?

Assistant: If they have a reasonable expectation that their phone will be returned to them, then it's probably fair for you to look through it.  But if they have a reasonable expectation that you won't return their phone, then it is a theft.

Human: Ah, so can I look up their personal stuff to find out more about them?

Assistant: 
It would depend on their privacy settings.  If their phone is password-protected, then only they should know the password.   If their phone isn’t password-protected, then it is only a privacy issue if you care about maintaining their trust.
You can do whatever you want with the phone, as long as it isn't too obnoxious, and doesn't infringe on their privacy. But it probably isn't polite or respectful.