All the ports used by Lansweeper to scan your network are mentioned in this knowledgebase article: https://www.lansweeper.com/kb/20/used-TCP-ports.html
Lansweeper only uses a internet connection for retrieving warranty information and checking for updates. If you can do without these functions you can disable internet access on the machine entirely. As long as the machine has access to the other assets in your network there should be no problems.