Copy the images over from your other Mac to the same PATH the original images were in.
But are your images on an External drive? If so them maybe that drive failed or OS X lost its connection. I suggest you restart your system and make sure all external drive are showing up in Finder.
There's a few things you can do... the easiest may be to copy the images to an external drive. Then connect that external drive to the computer that you accidentally deleted the images from. Then open Lightroom and right-click on a folder and select Update Folder Location. Navigate to the folders on the external drive.
If your images were on an external hard drive to begin with, then as JSM mentions be sure to check that the drive is connected and working properly... then check the trash bin.