Does covering the pot really make water boil faster?
When you heat water in an open pot, some of the energy that could be raising the temperature of the liquid escapes with the vapor. But as long as more energy is being added to the water than is being lost with the vapor, the temperature will continue to rise until the water boils. Covering the pot prevents water vapor from escaping, enabling the temperature to rise more quickly. How much more quickly? In our experience, not a lot.
When we brought 4 quarts of water to a boil in covered and uncovered stainless steel Dutch ovens, the covered pot boiled in just over 12 minutes and the uncovered pot boiled in 13 minutes and 15 seconds. But why waste even a small amount of heat when it’s so easy not to? That said, since you’re not losing time or energy until the water begins to steam, put the water on to heat first and then go hunting for the lid.