According to the Valence Shell Electron Pair Repulsion (VSEPR) theory, the magnitude of repulsive interactions between electron pairs follows the order: Lone pair (lp) – Lone pair (lp) > Lone pair (lp) – Bond pair (bp) > Bond pair (bp) – Bond pair (bp) .

To determine which molecule has the maximum lone pair - lone pair repulsion, we count the lone pairs on the central atom of each molecule:

1. $XeF_2$: Xenon (group 18) has 8 valence electrons. Two are used for bonding, leaving 6 electrons which form 3 lone pairs .
2. $ClF_3$: Chlorine (group 17) has 7 valence electrons. Three are used for bonding, leaving 4 electrons which form 2 lone pairs .
3. $IF_5$: Iodine (group 17) has 7 valence electrons. Five are used for bonding, leaving 2 electrons which form 1 lone pair .
4. $SF_4$: Sulphur (group 16) has 6 valence electrons. Four are used for bonding, leaving 2 electrons which form 1 lone pair .

Since $XeF_2$ has the highest number of lone pairs (3), it will experience the maximum 'lone pair - lone pair' electron repulsions among the given options.