The paper is related to the classical theorem of Lyapunov which says that an \(R^n\)-valued atomless \(\sigma\)-additive measure on a \(\sigma\)-algebra has a convex range. \textit{G. Knowles} [SIAM J. Control 13, 294--303 (1974; Zbl 0302.49005)] generalized this theorem for non-injective measures with values in locally convex spaces. \textit{P. de Lucia} and \textit{J. D. M. Wright} [Rend. Circ. Mat. Palermo, II. Ser. 40, No. 3, 442--452 (1991; Zbl 0765.28011)] introduced the concept of convexity in topological groups and -- with suitable modification of the definition of non-injectivity -- transferred Knowles result to the case of group-valued measures. In the main result of the paper under review, this theorem of de Lucia and Wright is generalized for modular functions on complemented lattices.