They offer ISO-images for these updates too. You can also create a USB-bootable version from these using the geteltorito tool (which is available via apt).
https://workaround.org/article/updating-the-bios-on-lenovo-l...
Edit:
> OK, so all these problems are all due to my specific situation (running dual boot
Why are you using GRUB to dual-boot at all? Your machine has UEFI for that.