It's not a driver problem. Bootloaders need to have an elementary understanding of physical hardware to see and present stuff for boot. When you boot from USB (which the bootloader understands) you end up in the kernel initramfs which has drivers/support for the eMMC/SD card so you can see it as an install target. Once you reboot and attempt to boot directly from that the eMMC/SD hardware (which the bootloader doesn't support or understand) .. you don't boot.
Hence the suggestion of using another bootloader. If you can boot an Ubuntu LiveUSB image on your device; whatever version of GRUB that the LiveUSB is using works on your hardware and you can use that to boot LE. The only thing you'll need to figure out is the GRUB boot config, but that's never too hard and there's probably some posts in this forum on the topic (i'm being lazy and not Googling it for you).