The pair of xenon compounds, which have a same number of lone pairs of electrons on the central atom is

$\left(1\right) {\mathrm{XeO}}_3$: Xenon contains $8$ electrons in its valence shell, $6$ electrons are used in bonding with three oxygen atoms and $2$ electrons remain unbonded, i.e., $1$ lone pair of electrons.

$\left(2\right) {\mathrm{XeF}}_6$: Xenon contains $8$ electrons in its valence shell, $6$ electrons are used in bonding with six fluorine atoms and $2$ electrons remain unbonded, i.e., $1$ lone pair of electrons.

$\left(3\right) {\mathrm{XeF}}_2$: Xenon contains $8$ electrons in its valence shell, $2$ electrons are used in bonding with two fluorine atoms and $6$ electrons remain unbonded, i.e., $3$ lone pairs of electrons.

$\left(4\right) {\mathrm{XeF}}_4$: Xenon contains $8$ electrons in its valence shell, $4$ electrons are used in bonding with four fluorine atoms and $4$ electrons remain unbonded, i.e., $2$ lone pairs of electrons.

$\left(5\right) {\mathrm{XeOF}}_4$: Xenon contains $8$ electrons in its valence shell, $4$ electrons are used in bonding with four fluorine atoms and $2$ electrons are used in bonding with one oxygen atom and $2$ electrons remain unbonded, i.e., $1$ lone pair of electrons.

Hence, the pair of xenon compounds, which have a same number of lone pairs of electrons on the central atom is ${\mathrm{XeO}}_3$ and ${\mathrm{XeF}}_6$.