No, neither the L-12 nor the L-20 support moving tracks aside from export to USB flash drive, (optionally deleting the track in the project,) and then importing from the USB flash drive to a different empty track.
I created an app for one-way L-12 to L-20 project migration:
https://github.com/sean-e/LivetrakPort
My notes on the L-12 and L-20 project files are here:
https://github.com/sean-e/LivetrakPort/blob/master/zdt.md
Someone could work with what's there to implement a reverse migration.
The L-12...