The Los Angeles Board of Zoning Appeals will conduct a hearing Tuesday on the approval of a building permit for renovation of the Westside Racquet Club. The Cheviot Hills Homeowners Assn. and a group of independent homeowners asked the board to reconsider the city's issuance of a building permit for the project. The homeowners want the city to impose additional conditions before allowing construction to go ahead. The zoning board is scheduled to meet at 12:30 p.m. in hearing room 350, 200 N. Spring St.