  We show that the knot lattice homology of a knot in an L-space is equivalent
to the knot Floer homology of the same knot (viewed these invariants as
filtered chain complexes over the polynomial ring Z/2Z [U]). Suppose that G is
a negative definite plumbing tree which contains a vertex w such that G-w is a
union of rational graphs. Using the identification of knot homologies we show
that for such graphs the lattice homology HF(G)$ is isomorphic to the Heegaard
Floer homology HF^-(Y_G) of the corresponding rational homology sphere Y_G.
