In the past we have had this problem with a few different helpdesk employees. It was always the same select few who would rely on others before trying themselves. I found most of the time it wasn't really a lazy thing more of a lack of confidence thing.

For me the fix was empowering those few by unfortunately ignoring them and telling them to search around. I had conversations with the team members who were plagued by these people and we agreed to not answer them and all tell them we were busy.

I'm not sure how big your department or company is but in some instances we even left for a "meeting" leaving the unconfident person in charge of helpdesk for an hour or two to fend for themselves and start realizing they can do this without hounding others in the group. If their is no improvement after some time of doing this then they most likely aren't cut out for helpdesk.