The adapter issue with Luna only applies to the Luna Dongle and its Thunderbolt option through USB-C from a Mac as explained in the very link you provide above. IE you cannot use an adapter to go from the USB-C port on a Mac to the mDP port the Luna dongle uses since the adapters don't support the mDP protocol, the dongle uses.
It is not related to the way you are connecting the iPad, just the Luna Dongle.
Since your 2012 Mac does not have USB-C ports this point is moot. You are connecting the Luna dongle directly to the Thunderbolt Port on the Mac. Your Mac has the required port, it needs no adapter for it.
https://faq.lunadisplay.com/article/60-usb-ethernet-connection
Basically the USB adapter provided above should work over the standard USB connection. Once you have the Apps downloaded on both devices, and the Luna dongle connected to the TB/mDP port.
You'll need to have the Luna Apps running on both Mac and iPad. Then follow the onscreen prompts on the Luna Apps.
You cannot use the Luna USB-C dongle with non USB-C Macs.