it seems like all that does is make a new initrd.
Well, gee, that’s the whole point.
Your original initrd image apparently does not contain lvm support, so you need to make an initrd image that does.
When you boot into rescue mode, successfully mount/chroot and make a new initrd image, the new initrd image should contain everything that is need to boot the installation that you have mounted/chrooted.
If it doesn’t, then you need to determine what module(s) is/are missing, load it/them and then add it/them with the appropriate --preload or --with options when you run mkinitrd. Normally, you only need those options when you are making a new initrd image before you modify the setup and want to build in enough new features to allow the new setup to boot.