The relationship between lattice energy, hydration energy, and solubility limits is a foundational thermodynamic principle of solutions, so no citation is needed.
The claim states that the solubility limits of salts in water are determined by thermodynamic equilibrium between lattice energy and hydration energy. This is a fundamental, textbook thermodynamic definition taught in general chemistry regarding ionic solubility (the Born-Haber cycle and free energy of solution). It constitutes common knowledge regarding solution chemistry, so no literature citations are required.