  We investigate the electronic structure of a recently discovered, heavily
electron-doped iron based superconductor LaFe$_2$As$_2$. Although first
principles calculation shows apparent absence of hole Fermi surfaces around the
$\Gamma$ point, we reveal, by hypothetically removing the La $d$ orbital
contribution, that a hole Fermi surface around the $\Gamma$ point is
essentially present. In the collapsed phase of LaFe$_2$As$_2$, which is
non-superconducting, the hole Fermi surface is found to be absent, and the
difference from the uncollapsed superconducting phase can be naturally
understood within the spin-fluctuation mediated pairing scenario.
