The expression, $$\Delta {\text{G}} = {\text{nRT}}.l{\text{n}}\frac{{{{\text{P}}_2}}}{{{{\text{P}}_1}}},$$    gives the free energy change

We know, the property relation:
$$dG = vdp - sdT$$
Which is valid for both reversible and irreversible process since it is a property relation. when the system undergoes isothermal change $$dT = 0$$
$$\eqalign{ & {\text{So, }}dG = vd \cr & \Rightarrow dG = \frac{{nRT}}{P}dP\left( {{\text{for, ideal gas}}} \right) \cr} $$
On, integration
$$ \Rightarrow \Delta G = nRT.ln\frac{{{P_2}}}{{{P_1}}}$$
So, for a system containing ideal gas and undergoing isothermal change of volume or pressure this expression is valid.