the answer: They represent different states of the same substance.
The student was not successful.
Consider the standard reduction potentials.
Li⁺ + e⁻ ⇌ Li; E° = -3.04 V
2H₂O + 2e⁻ ⇌ H₂ + 2OH⁻; E° = -0.83 V
To reduce Li⁺ to Li, the student must apply 3.04 V.
However, it takes only 0.83 V to reduce water to hydrogen.
Thus, the student will get H₂ instead of Li.
She should make soup. When you are way above sea level, the atmospheric pressure decreases. Boiling starts when the vapor pressure of the liquid is the same with the atmospheric pressure. This would mean that water boils at a much lower temperature than the usual 100deg C. So it would take longer for the components in the soup to cook compared to when it is cooked on the foot of the mountain.