The Live-Cd (on usb stick) will give you the working environment needed to create a chroot environment to install grub from the installed system, I have outlined the procedure in this post which might help, but one more thing you would need to do is mount the efi partition in the chroot environment to be able to install grub to it
My efi boot partition is sda2 so I would mount it using this (in the linked post example)sudo mount --bind /dev/sda2 $TARGET/boot/efi
One thing to check would be that grub-efi is installed in the chroot, if not it can be easily installed with
and then grub installation would be like this
After this has completed you can exit the chroot and unmount it then reboot the system, hopefully it will give you the boot entry you need.
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