The lattice energy depends on 2 factors:
1)effective packing.
2)ionic force of attraction
As cations generally occupy voids in crystalline lattice they should have smaller size than anions.
Ionic force of attraction increases when the cation size is large and anion size is small.
In most cases the most effective match of both factors is found when size of both ions is same.However sometimes there is deviation.
In carbonates the anion is quite large and the voids are large enough to accommodate all the cations given.
therefore the Lattice Energy mainly depends on ionic force of attraction which is in the order. K>Na>Li
In LiF and LiBr:
LiBr shows high tendency of covalence which dominates over effective packing.Therefore due to less ionic force of attraction LiBr has less lattice energy.