It's important to note that software installations and software license keys are not directly related as far as Lansweeper is concerned. This is because they are scanned from different sources, as further explained in
this article. This means that, if you're able to scan a certain software doesn't necessarily mean its product key will also be scannable.
Most software license keys are scanned using the registry locations set up under Software\License Key Settings, on this page you can enable the scanning of the keys already present and add to them. For more information on license key scanning you can check
this article.
For scanning adobe license keys specifically, the registry and .swidtag files can be used, swidtag files are scanned automatically if found. These .swidtag files are commonly found under %programdata%. If these .swidtag files are not present the only remaining option is scanning they keys from the registry, you may need to manually add a location for this under Software\License Key Settings.