Under
Configuration\Product Keys you can see the key where Lansweeper searches for the product key. This is not a list of scanned data, but a library. You need to enable product key scanning for the products you are interested in. Actual scanned keys can be found on computer asset pages under tab
Software or in the report "License: Software licensekey overview". Product keys are rescanned once every 40 days by default. In order to immediately update all data on a specific computer, open its asset page, hit
Rescan asset and wait until the scan finished.
Details on viewing and scanning product keys can be found in
this KB article.