Why does aluminum chloride have a higher lattice energy than aluminum fluoride?
Lattice energy is a function of the radius ratio, which when tends to 1, improves the packing efficiency of the molecule. Here the radius ratio of the chloride ions and aluminium ions is much closer than the fluoride ions.
You could think of this from the born habers cycle also. Where the electron affinity of chlorine is higher, which leads to overall higher lattice energy. However, the radius ratio logic is much more convincing as the habers cycle logic would require the other parameters like the heat of formation also