Reason of lanthanoid contraction is: 

The formation of the oxide ion ${\mathrm{O}}^{2-} \left(\mathrm{g}\right)$ requires first, an exothermic and then an endothermic step as shown below:

$\mathrm{O} \left(\mathrm{g}\right)+{\mathrm{e}}^{-}\to {\mathrm{O}}^{-} \left(\mathrm{g}\right); \mathrm{\Delta H}=-142 \frac{\mathrm{kJ}}{\mathrm{mol}}$,

${\mathrm{O}}^{-} \left(\mathrm{g}\right)+\mathrm{e}\to {\mathrm{O}}^{2-} \left(\mathrm{g}\right); \mathrm{\Delta H}=844 \frac{\mathrm{kJ}}{\mathrm{mol}}$.

This is because: