Carlyle Falkenborg, 65, who served as mayor of Duarte four times, died Saturday of lung cancer. Falkenborg, a retired customer service representative for Pacific Telephone Co., served on the City Council for 12 years until his defeat last April. Earlier he had served on the Duarte Unified School District board. Falkenborg, who lived in Duarte for 35 years, is survived by three children. They have requested that donations be made to the American Cancer Society.