

First, of course it is completely fine for /home to be on another drive. As long as it is configured in /etc/fstab correctly, almost any configuration of drives and partitions is okay.
Second, your boot issue sounds very strange. Firstly, x220 has a traditional bios boot, right? So you do not need an /EFI partition, and should install grub to the reserved space on the drive for booting (which if you configured MBR for your drive requires no change, if you configured GPT you need to reserve that space). If you have one of the x220s with libreboot (not sure if that exists, but I used to have an x200 with libreboot flashed for the bios), then your grub version might be very out of date, which could cause issues as well.
Looking online, I think x220 supports both legacy booting and UEFI. This could be a useful resource