Serial numbers are critical. You should take care to store them securely. A cardfile, a computer file stored on multiple discs, etc. If you happened to register Lightroom with the Adobe when you installed it, you can retrieve your serial number from your Adobe account. What operating system do you use? Your Lightroom license entitles you to two installations, but those installations are not monitored for Lightroom like they are for Photoshop.
Thank you!! I found it in my account under purchases! This makes me very happy!!