The quantity of Heat Energy (Q) released on cooling a heated substance depends on its Mass (M), specific heat capacity (C), and change in temperature (Φ)
Thus, Q = MCΦ
Since, M = 45.4 g
C = 3.56 J/g°C,
Φ = 250°C - 25°C = 225°C
Q = 45.4g x 3.56J/g°C x 225°C
Q= 36365.4 Joules
Thus, 36365.4 Joules of heat energy is released when the lithium is cooled.
There’s no formula that relates solubility to temperature, but you can look up the solubility constant Ksp of substance given and then take the square root of that to find solubility.