In the present paper, we introduce the notion of $(F,G)$-derivation on a lattice as a generalization of the notion of $(\wedge,\vee)$-derivation. This newly notion is based on two arbitrary binary operations $F$ and $G$ instead of the meet $(\wedge)$ and the join $(\vee)$ operations. Also, we investigate properties of $(F,G)$-derivation on a lattice in details. Furthermore, we define and study the notion of principal $(F,G)$-derivations as a particular class of $(F,G)$-derivations. As applications, we provide two representations of a given lattice in terms of its principal $(F,G)$-derivations.