We observe that two types of congruence are introduced in a distributive lattice, one in terms of ideals generated by derivations and the other in terms of images of derivations. Also we undertake an equivalent condition is derived for the corresponding quotient algebra to become a Boolean algebra. An equivalent condition is obtained for the existence of a derivation. We grasp that the set of all isotone derivations in a distributive lattice can form a distributive lattice. Moreover, we identify the fixed set of derivations in lattices and prove that the fixed set of a derivation is an ideal in lattices. Keywords: Derivation, kernel, congruence, ideal, kernel element