Before participants can control your shared desktop, they must be LiveMeeting Presenters. There are 2 ways to do that.
BEFORE MEETING: Send them the "Join as Presenter" link (instead of "Join as Attendee") OR
IN MEETING: From the "Attendees" menu, right-click on the Attendee name and choose "Promote to Presenter." (They'll get confirmation and their LiveMeeting icon changes.)
Once the user's a Presenter, there are 2 ways to give them control.
AS HOST: The LiveMeeting menu bar has 4 icons, including "Give Control." Choose "Give Control" and a list of Presenters appears. Pick the user who needs control.
AS VIEWER: Open the "Content" menu, which shows everything shared by the host. They can right-click on your "Desktop" and pick "Request Control" from the pop-up menu. A request appears on the host screen, which you accept.
Either of these should give desktop control to LiveMeeting attendees, once they're promoted to a Presenter.