Contact Adobe Support thru chat and ask them to reset your activations. That will recover the lost installation's activation for another use... but it will also deactivate the current installation so you will need to reactivate that afterwards.
Chat support - For the link below click the Still Need Help? option in the blue area at the bottom and choose the chat option...
Make sure you are logged in to the Adobe site, have cookies enabled, clear your cookie cache. If it fails to connect try using a different browser.
Serial number and activation chat support (non-CC)
https://helpx.adobe.com/contact.html?step=PHSP-PHXS_downloading-installing-setting-up_licensing-activation_stillNeedHelp
Download and Installation Help -
https://helpx.adobe.com/download-install.html
Lightroom 6
https://helpx.adobe.com/lightroom/kb/lightroom-downloads.html