We prove extension theorems for group-valued modular functions defined on orthomodular lattices or modular complemented lattices and for modular measures defined on (pseudo-)D-lattices generalizing results of B. Rie\v can (\cite{R69}, \cite{R70}, \cite{R79}), A. Avallone and A. De Simone \cite{AS} and A. Avallone, A. De Simone and P. Vitolo (\cite{ASV}, \cite{ASV2}). As basic tool we first prove an extension theorem for lattice uniformities. This also yields as immediate consequence a result on the extension of modular function on arbitrary lattices similar to that of G. Fox and P. Morales \cite{FM73} and P. Kranz
