  We study the localization properties of generalized, two- and
three-dimensional Lieb lattices, $\mathcal{L}_2(n)$ and $\mathcal{L}_3(n)$, $n=
1, 2, 3$ and $4$, at energies corresponding to flat and dispersive bands using
the transfer matrix method (TMM) and finite size scaling (FSS). We find that
the scaling properties of the flat bands are different from scaling in
dispersive bands for all $\mathcal{L}_d(n)$. For the $d=3$ dimensional case,
states are extended for disorders $W$ down to $W=0.01 t$ at the flat bands,
indicating that the disorder can lift the degeneracy of the flat bands quickly.
The phase diagram with periodic boundary condition for $\mathcal{L}_3(1)$ looks
similar to the one for hard boundaries. We present the critical disorder $W_c$
at energy $E=0$ and find a decreasing $W_c$ for increasing $n$ for
$\mathcal{L}_3(n)$, up to $n=3$. Last, we show a table of FSS parameters
including so-called irrelevant variables; but the results indicate that the
accuracy is too low to determine these reliably. \end{abstract}
