Other Lumina screen resolution

I have a system with Lumina installed but the highest screen resolution it allows is 1024 x 768.

This is running on a ThinkPad T420 which supports 1366 x 768 or 1600 x 900.

I did install Lumina whilst the disk was attached to a different system, so I don't know if that accounts for this.. How can I get support for a higher resolution?
That sounds like you are using the VESA driver rather than something Lumina related. Try switching to another driver like intel, nvidia, radeon, or "scfb" (if you installed/booted with EFI) depending on your hardware, and then you should be able to use the monitor's native resolution.
I have no idea about how to switch video drivers, I'm essentially a command line user ;)...

I'm not even sure how to tell which graphics chip is in use...

The system is running FreeBSD 11.0-RELEASE on a ThinkPad T420 using a 120GB MBR disk.