Soooo it sounds as if you want to use the internal LUA as a failover update point in the event the GUPs are unavailable.
This is perfectly possible, just not in the way that you're thinking. Just to break it down for you, in the LU Settings Policy you have:
Server settings: This tells the client where to update from (SEPM/GUP/LUA/3rd Party)
With the LiveUpdate option enabled, you then gain access to the Schedule and Advanced Tabs on the left pane. These additional tabs only affect the LiveUpdate portion of the client (sepliveupdate,exe so to speak). And these must be set to tell a client when to try to run a LiveUpdate attempt to your internal LUA (so are pretty important).
By default, the schedule is set to run every 4 hours, and so that client will not perform a LiveUpdate until they are both more than 2 days out of date and have not been in contact with the SEPM for more than 8 hours. I'd recommend having a play around with these "Options for Skipping LiveUpdate".
Just be aware that without these settings, then the clients will attempt a liveupdate on the schedule specified, regardless of whether or not they are in active communications with a working GUP&SEPM, potentially generating more traffic than is necessary (i.e. it will work how it did in SEP11).
Finally, the advanced tab allows you to choose if the users are able to initiate the liveudpate attempt manually amongst other options. With the "Allow users to run LiveUpdate" option enabled, the users will be able to kick it off from the SEP Client Console, by clicking "LiveUdpate" on the left (it will no longer be greyed out).