  We investigate the issue of eigenfunction localization in random fractal
lattices embedded in two dimensional Euclidean space. In the system of our
interest, there is no diagonal disorder -- the disorder arises from random
connectivity of non-uniformly distributed lattice sites only. By adding or
removing links between lattice sites, we change the spectral dimension of a
lattice but keep the fractional Hausdorff dimension fixed. From the analysis of
energy level statistics obtained via direct diagonalization of finite systems,
we observe that eigenfunction localization strongly depends on the spectral
dimension. Conversely, we show that localization properties of the system do
not change significantly while we alter the Hausdorff dimension. In addition,
for low spectral dimensions, we observe superlocalization resonances and a
formation of an energy gap around the center of the spectrum.
