  We study the effect of isoelectronic doping and external pressure in tuning
the ground state of the honeycomb iridate Na$_2$IrO$_3$ by combining optical
spectroscopy with synchrotron x-ray diffraction measurements on single
crystals. The obtained optical conductivity of Na$_2$IrO$_3$ is discussed in
terms of a Mott insulating picture versus the formation of quasimolecular
orbitals and in terms of Kitaev-interactions. With increasing Li content $x$,
(Na$_{1-x}$Li$_x$)$_2$IrO$_3$ moves deeper into the Mott insulating regime and
there are indications that up to a doping level of 24\% the compound comes
closer to the Kitaev-limit. The optical conductivity spectrum of single
crystalline $\alpha$-Li$_2$IrO$_3$ does not follow the trends observed for the
series up to $x=0.24$. There are strong indications that $\alpha$-Li$_2$IrO$_3$
is less close to the Kitaev-limit compared to Na$_2$IrO$_3$ and closer to the
quasimolecular orbital picture. Except for the pressure-induced hardening of
the phonon modes, the optical properties of Na$_2$IrO$_3$ seem to be robust
against external pressure. Possible explanations of the unexpected evolution of
the optical conductivity with isolectronic doping and the drastic change
between $x=0.24$ and $x=1$ are given by comparing the pressure-induced changes
of lattice parameters and the optical conductivity with the corresponding
changes induced by doping.
