Let \(a, b\) be elements of a poset \((P, \leq).\) Let \(U(a, b) := \{ x\in P; a\leq x \;\& \;b\leq x\},\) \(L(a, b) := \{ x\in P; x\leq a \^^M\&\;x\leq b\}.\) The poset \((P, \leq)\) is called a \(\lambda \)-poset if there is a (fixed) choice function \(\lambda \) such that \(\lambda (L(a, b)) = a\) and \(\lambda (U(a, b)) = b,\) provided \(a\leq b.\) A \(\lambda \)-lattice is an algebra \((P, \cdot , +)\) where \(\cdot \) and \(+\) are idempotent and commutative operations on \(P,\) satisfying the two distributivity laws and such that \(a\cdot ((a\cdot b)\cdot c) = (a\cdot b)\cdot c\) and \(a + ((a + b) + c) = (a + b) + c\) for every \(a, b, c\in P.\) The theorems in the first section establish the basic correspondence between \(\lambda \)-posets and \(\lambda \)-lattices. The second and the third sections deal with ideals, strong ideals and congruences on \(\lambda \)-lattices. The Theorem 3.2 gives an analogue of the Grätzer-Schmidt criterion on lattice congruences for congruences on \(\lambda \)-lattices. Theorem 3.3: The lattice Con \(P\) of all congruences on a \(\lambda \)-lattice \(P\) is distributive.