How does said software get "flashed" onto the hardware?
The UEFI applications that you can build with Lil UEFI can be shoved into a special FAT32 partition on your disk and named EFI/BOOTX64.EFI[1], the firmware finds this file and will start executing it.
[1]: It can be named something else so long as you tell the firmware about it in advance. I think that you can also load them via netboot.
In a DIY environment, https://www.flashrom.org/ or TL866 or something.