I assume you can a route like this for the LTE.
ip route 0.0.0.0 0.0.0.0 Dialer1
Is that route installed even when the LTE is down? If not, you add something like this with a higher admin distance.
ip route 0.0.0.0 0.0.0.0 10.1.1.1 240
If it is in the table when the dialer interface is down, you will have to do something with IP SLA to make that route to the dialer interface conditional.