An identity in the language of lattices is trivial if it holds
in all the lattices. We show that, for every nontrivial identity e
in the language of lattices, there exists a natural number n such that
e fails in the lattice of lambda theories of lambda calculus
with n added constants. The same result is not true for quasi-identities:
we show that the lattice of lambda theories satisfies nontrivial
quasi-identities.