Which version are you using?
For the CC version you simply launch Creative Cloud on the other machine, then go to the Apps tab and click the install button next to LR. For the stand-alone version of LR6 you could copy the original download package if you still have it.
For example on Windows the download usually extracts to the desktop. You could copy the folder to a disk or external drive. Then open the folder on the other computer and double-click on Setup – see image below. On Mac OSX you should be able to copy the dmg package from the downloads folder in Finder.
If you want to download again you could try from here:
N.B. after completing installation go to the LR menu and click:
Help >> Updates
Then install the 6.0.1 patch.