  We study the strong Nakano property in Banach lattices with a special focus
on free Banach lattices. We show that for every finite dimensional Banach space
$E$, the free Banach lattice $FBL[E]$ has the strong Nakano property with a
constant independent of the dimension. It is also shown that if $FBL[E]$ has
the strong Nakano property, then $E$ cannot contain subspaces isomorphic to
neither $c_0$ nor $L_1$.
