Vernon Munroe Jr., a corporate lawyer who had been a senior partner in the Manhattan law firm of White & Case, died at his home on the Upper East Side of Manhattan. He was 84. He had Parkinson's disease, his family said. Mr. Munroe was born in Englewood, N.J. He graduated from the Phillips Exeter Academy in Exeter, N.H., and from Harvard. In 1936, he graduated from Harvard Law School and joined White & Case. Mr. Monroe served in government agencies and the Navy during World War II. He became a partner at White & Case in 1952, going on to head its Paris office from 1963 to 1966. He retired in 1978. Mr. Munroe was the widower of Gretel Zinsser. He is survived by his second wife, the former Ofelia Lopez y Bosque; two daughters, Gretel Munroe of Framingham, Mass., and Antonia Grumbach of Manhattan, and two grandchildren.