Mr. Mrs. Jervis Campbell Webb of Riverdale, N.Y., Detroit, and Palm Beach announce the engagement of her daughter, Charlotte Dobson Lyeth to Michael A. Dively of Tranverse City, Mich. Mr. Dively served three terms in the Michigan State Legislature.

Miss Lyeth is the daughter of the late John William Clarke of Evanston, Ill. and the adopted daughter of the late J.M. Richardson Lyeth Jr. of New York. A graduate of Principia School (Mo.) and Principia College (III), she made her debut in 1961 at the international Garden Club and at a private tea-dance. She worked in the 1968 and 1972 Presidential campaigns as a staff assistant to the postmaster general and later as governmental liaison for the Advisory Council on Historic Preservation in this city. Presently with the Capital Fund Office at the New York Botanical Garden, the future bride also serves on the board of the Longyear Realty Corporation, MArquette, Mich., the Women's National Republican Club, the Neighborhood Playhouse COmpany, and is a member of the New York Junior League. Her step-father is chairman of the board of the Jervis B. Webb Company in Detroit, and her grandparents are the late Mr. and Mrs. Frederick Clifford Desmond Dobson, and the late Mr. and Mrs. Harley F. Clarks, all of Evanston, III.

Mr. Dively is a partner in the Traverse City law firm of Olsen, Dively, and Walton. The son of Mr. and Mrs. George S. Dively of Cleveland and Boca Raton, Fla. and the late Harriet Seeds Dively, graduated from the University School in Cleveland, Williams College, and received his law degree from the University of Michigan. While serving in the Michigan State Legislature, he was also on the White House COuncil on Youth. Mr. Dively was appointed by the governor as the deputy director of the Michigan Department of COmmerce and later was the director of the Energy Administration. His father is honorary chairman of Harris Corporation in Cleveland and he is the grandson of the late Mr. and Mrs. Michael A. Dively of Claysburg, Pa. and the late Mr. and Mrs. Hugh Seeds of Altoona, pa. A June wedding is planned.