I 1 is implicative and lower-bounded. One can verify that there exists a lattice which is Heyting. A Heyting lattice is a Heyting lattice. Let us note that there exists a lattice which is Heyting and strict. Let L be a lower bound lattice.
L is finite.
Let us mention that every lattice which is finite is also bounded. Let us note that every lattice which is distributive and finite is also Heyting.