Lio (in his black form) evaporates the Frozen Lake just by coming in contact with it. The average height of an American man is 5 feet 9 inches, or 1.7526m.
1 pixel = 1.7526m/13 = 0.134815385m
0.134815385m X 2880 = 388.268309m
388.268309m/2 = 194.134154m
Next up is the depth. Due to the cracks that appear from the melting, we can ascertain the ice goes all the way down.
1 pixel = 388.268309m/2829 = 0.137245779m
0.137245779m X 385 = 52.8396249m
The scaling's not entirely perfect, but that's the best I could get with the shots available, and keep in mind that there's also Deus Promith's lab at the bottom. Volume as a spherical cap.
V = π/3H^2(3R = H)
= π/3 X 52.8396249^2(3 X 194.134154 - 52.8396249)
= 1548337.28m^3
Ice weighs 919kg/m^3.
M = 1548337.28 X 919
= 1.42292196e9kg
It takes 333.55 kilojoules to melt 1kg of ice.
E = 1.42292196e9 X 333.55
= 474615619758 kilojoules
= 4.7461562e14 joules
But the ice doesn't just melt; it evaporates, so let's also add the energy to vaporize the water (more information on which can be found here).
E = 1.42292196e9 X 2.26 X 10^6
= 3.21580363e15
Finally, to add the two together to get our final results.
E = 4.7461562e14 + 3.21580363e15
= 3.69041925e15 joules
= 882.0313695028680741 kilotons
Final Results
Lio melts the frozen lake = 882.031 kilotons
