When a person communicates directly with the mayor or any county commissioner, whether orally, in writing, electronically, or otherwise, in an effort to get the board to approve or disapprove something such as an ordinance, resolution, contract, development permit, etc., that's lobbying. Even if a board member initiates the discussion, it is still lobbying. Even if the meeting happens off campus (at a golf course, restaurant, party, grocery store), it is still lobbying.
Trying to influence the decision-making of a constitutional officer such as the sheriff or the tax collector is NOT lobbying. Generally, talking to county staff does not constitute lobbying. However, if one talks to staff in such a way as to attempt to communicate indirectly with a county commissioner or with the mayor (for example, asking a member of the mayor's staff to urge him to vote a certain way on a pending board matter), that is lobbying.