If the hydration energy is greater than the lattice energy, then the enthalpy of solution is negative (heat is released), otherwise it is positive (heat is absorbed).
The hydration energy should not be confused with solvation energy, which is the change in Gibb's free energy (not enthalpy) as solute in the gaseous state is dissolved. If the solvation energy is positive, then the solvation process is endergonic; otherwise, it is exergonic.
For instance, water warms when treated with CaCl (anhydrous calcium chloride) as a consequence of the large heat of hydration. However, the hexahydrate, CaCl·6HO cools the water upon dissolution. The latter happens because the hydration energy does not completely overcome the lattice energy, and the remainder has to be taken from the water in order to compensate the energy loss.
The hydration energies of the gaseous Li, Na, and Cs are respectively 520, 405, and 265 kJ/mol.