What do these problem users see when accessing the Lansweeper web console? An access denied page that lists the users' user groups and web console privileges? If so, did you add the individual user accounts or a user group the users belong to to the Configuration/Website Management/Website Access section of the Lansweeper web console?
Submit user groups with the format NetBIOS domain name\group name, individual users with the format NetBIOS domain name\username and separate user/group entries with commas.
Note that you should no longer add user groups directly to your web.config file. This was the old way of doing it, under Lansweeper 4.X. In Lansweeper 5.X, you must submit your groups and users in the Lansweeper web console.