A new branch of mathematical chemistry, known as chemical graph theory which deals with the non trivial applications of graph theory to solve molecular problems. A topological index of a graph is a real number which is fixed under graph isomorphism. The forgotten topological index or F-index of a graph is defined as the sum of cubes of the degree of all the vertices of the graph. In this paper we study the F-index of four operations related to the lexicographic product on graphs.