Unfortunately the only way your app can receive a notification in "production" mode is once it's published in the app store. There isn't a way to get a production token unless your app is signed with the app store certificate.
The only thing that should use "live" is when you're signing the app with an app store certificate. Push notifications for AdHoc distribution should be in "dev" mode.
My experience shows that what the original asker wants is what works... Signing an adhoc project with LQPushNotificationModeDev does not work, and signing with LQPushNotificationModeLive does.
Anyone figure out how to get push to work on adhoc? Works fine on development profile but not for adhoc. I've tried LQPushNotificationModeLive and LQPushNotificationModeDev for adhoc and neither work.