Why does covalent nature in ionic solids increase the lattice energy?
(First of all I have to note that I'm just a student, not a specialist in solid body physics or chemistry)

Let's consider chemical bond in general, starting with diatomic molecule (our findings for this case we will generalize to crystalline structure later):

When we say that chemical bond is formed, we mean that for electrons of each atom by atomic interaction (interaction of atomic orbitals of each atom to each other) become available to be situated on molecular orbitals(MO) (defining as superposition with different contributions of atomic orbitals(AO)). Now we must say that depending from atomic orbital energy and its symmetry, result of interaction with another AO may be different.
If we have two interacting AOs with big (bigger than stated value) difference in energies it leads to formation of two MOs: one of them, bonding MO, must have energy closer to such AO that is lower by energy, another relatively must have energy closer to another AO (see picture). In this case we have low energy of stabilization (system weakly feel energy changing before and after interaction).
If difference as big as whole system looks like we give both electrons to one of AOs it means that electron density of bond is shifted to one of atoms. In this case we say that we deal with IONIC bond.
Now COVALENT bond: energies of interacting orbitals are close. This way we have big stabilization energy (see picture). Because of it we can say that covalent bond is stronger then ionic.

Simplifying: ionic bond is provided by Coulomb interactions (in approximation), but covalent bond is provided not only by them, and this is the reason why it's stronger.

Generalization to crystalline lattice: now we must consider group of interacting orbitals, but main findings remain the same: bond forming by AOs with same energy is stronger.

And, as lattice energy is energy of interacting particles forming lattice, it's clearly determined by MO's energy.

That's why I think yes, we may generalize your finding as a fact.