As long as you do not vote on a matter directly concerning your employer, your membership on the board is not considered executive branch lobbying.
However, an ethics issue is presented. The applicable ethics rule for the state board member is the conflict of interest rule (IC § 4-2-6-9). The conflict of interest rule does not apply to the employer of the state board member, only to the state officer, employee, or special state appointee who holds a state position. If a board member's employer has a business relationship with the board, then the employer is bound by the State Ethics Code when conducting business with the state board.
For more information, see the Executive Branch Lobbyist Registration Rule, or call (317) 234-4431.