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How can I safely move /lib to a mounted partition

I have made my root partition a long time ago and since I have var, home and usr in different logical volumes I made it quite small. Unfortunately /lib has grown quite a bit and my root partition is now full. I want to move /lib to a new lvm which I made and I’ve done the whole copying and all, but now I want to mount /dev/mapper/MySystem-lib /lib and also delete the original /lib in the root partition. I’ve already one managed to get myself stranded by moving /lib to /lib.old.

My question is two fold. If I put the mount in /etc/fstab and actually delete /lib on the root partition, will everything work? Since from my unfortunate mistake with the move, I’ve found out stuff like mount doesn’t work without lib.

And second how to I get to the point where I have deleted /lib and mounted /dev/mapper/MySystem-lib in it’s place?