The magnetic behaviour of ${\mathrm{Li}}_2\mathrm{O}$, ${\mathrm{Na}}_2{\mathrm{O}}_2$ and ${\mathrm{KO}}_2$, respectively, are

In the structure ${\mathrm{Li}}_2\mathrm{O}$ each lithium atom loses one electron to form 2 cations ${\mathrm{Li}}^{+}$ and oxygen atom gains two electrons to form the anion ${\mathrm{O}}^{2-}$.  It has no unpaired electrons. So, it is diamagnetic in nature. 

The peroxide ${\mathrm{O}}_2^{2-}$ present in  ${\mathrm{Na}}_2{\mathrm{O}}_2$ has 4 electron in ${\mathrm{\pi }}^{*}2\mathrm{p}$, thus all are paired. So, it is diamagnetic in nature.

In the structure ${\mathrm{KO}}_2$ oxygen is present in ${\mathrm{O}}_2^{-}$. The number of electrons present is 17, where the where the sixteen electrons are from two oxygen atoms and one from the negative charge. There is one unpaired electron present in the last orbital. Hence, it is paramagnetic in nature. 

${\mathrm{Li}}_2\mathrm{O}\to$ diamagnetic

${\mathrm{Na}}_2{\mathrm{O}}_2\to$ diamagnetic

${\mathrm{KO}}_2\to$ paramagnetic