Question

why are compounds of lithium more covalent than the corresponding compounds of sodium and potassium

Answer 1

Lithium compounds are covalent because of its high polarization power due to its small size.
Because of the high polarization power lithium tends to deviate the pair of electrons resulting in a covalent bond.

While the other elements of the group are comparatively larger than lithium hence their polarization power is low hence bond less covalent.