Answer
This is very likely a permissions issue rather than a genuine profile-configuration mistake. When a new Lobby page is first created, it's automatically granted only to one specific Permission Set, itself controlled by a System Parameter defining which permission set gets granted when a Lobby page is created. Check whether the affected end users' own Permission Sets actually include that specific granted permission set — if not, they won't be able to load the Lobby page at all, even though the Base Profile correctly points them at it as their home page.