I had a problem with a drive that would not mount, yet was seen by Disk Utility. It had been formatted and files copied to it on a different machine. The only solution was to use Disk Utility to reformat on the Mac that did not mount the disk. The disk was then immediately mounted and seen properly.
You will lose the images copied onto the disk of course but for now the drive is useless anyway, so no harm trying and if it works you can use your old Mac to re-copy the images.
As for the new iMac finding them in LR, this is done within the LR library at the top level directory where you will see a (?). Right click and select Find Missing Folder or equivalent, then navigate to your new drive, same folder.