Microsoft has released an authenticator app for Windows Phones, and third-party authenticator apps can be used for other platforms. Microsoft Authenticator can be enabled with your LastPass account, so that you enter your email address + master password, then a code generated by the multifactor app when logging in to your LastPass account.
Microsoft authenticator app is supported on Windows Phone 7 and Windows Phone 8 devices and is compatible with Google Authenticator.
The Microsoft authenticator app can be downloaded from the Windows app store here: http://www.windowsphone.com/en-us/store/app/authenticator/e7994dbc-2336-4950-91ba-ca22d653759b or by searching in the store on your device.
Then, in your LastPass Icon > My LastPass Vault > Settings > Multifactor Options tab, you can click the “Google Authenticator/DUO” option, click to display the barcode, then scan the barcode on your mobile device in your Microsoft authenticator app.
If you want to enable Multifactor authentication for your Microsoft account itself, you must do so from your account settings here: https://account.live.com/proofs/Manage