Import mail into windows 8.1 mail app?

Is there a way to import mail into windows 8.1 mail from windows live mail?

Not really. Where did your old mail originate? If it was IMAP then you can add the account and download everything again. If it was POP you could forward it to an IMAP account (like any MS account) - see here Using email accounts over POP on Windows 8.1 and Windows RT 8.1 - Windows Help

In my opinion WLM is far superior to the mail app - especially for searching, composing decent looking emails. I have both installed and use the mail app only for the notifications really as I can see at a glance if a new mail requires action.