How many Homomorphisms are there from one bounded lattice to another?

Question

for a project that I work on, I need to know how many homomorphisms there are from one finite lattice with 0 and 1 to another. I remember that I already worked it out if one of them is the trivial lattice {0,1}.

Any ideas?

In detail:

Take two bounded lattices

$L_1,0_1,1_1,\vee_1,\wedge_1$ and $L_2,0_2,1_2,\vee_2,\wedge_2$

Let $f\in Hom(L_1,L_2)$, then

1. $f(a\vee_1 b)=f(a)\vee_2 f(b)$
2. $f(a\wedge_1 b) = f(a)\wedge_2 f(b)$

And $f \in Hom_{01}(L_1,L_2)$ if

1. $f \in Hom(L_1,L_2)$ and
2. $f(1_1)=1_2$
3. $f(0_1)=0_2$

My question is:

What is $|Hom(L_1,L_2)|$ and $|Hom_{0,1}(L_1,L_2)|$ ?