Lime does not cause a blue color as it is a white color, however calcium sulfate may cause an aquamarine color.
The blue-green shade of the Havasupai falls water is caused by minerals in the river that coat the dirt, and rocks with a creamy-white travertine deposit (calcite). The whitened riverbeds reflect the color of the water, providing a turquoise contrast to the ruddy canyon walls.
Copper sulfide is insoluble and will also not cause blue water. You are thinking of copper sulfate.
You might consider more testing to determine the source of the blue water, in particular obtaining first flush and flushed samples will assist in locating the source of the corrosion.
If you have blue/blue-green stains sinks or plumbing fixtures, you should test your water for copper. To determine if
copper is present, arrange to test your drinking water at a certified laboratory. To evaluate the highest level of copper exposure, collect a sample when water has remained motionless or stagnant in the plumbing system for at least six hours. When collecting the sample, collect the first flush of water from the cold water faucet with the aerator removed. Do not allow any water to run before collecting the sample. This is called a first-draw or first-flush sample. This first-flush will contain the highest copper levels. After the tap has run for one minute, collect a second sample. This is called a flushed sample. The flushed sample provides a water sample that has not been in contact with the plumbing system for an extended period of time.
To interpret the results, consider both the copper concentrations and the comparison between the first-draw and flushed samples. If results show higher levels of copper in the first-draw sample than the flushed sample, the copper is most likely coming from corrosion
of household plumbing components, such as copper or brass fittings. On the other hand, if test results show nearly equal amounts of copper in both the first-draw and flushed samples, the copper is probably coming from a plumbing source outside the house, such as the well pump.
For treatment to increase the pH and eliminate the copper, consider a calcite treatment filter system for pH adjustment.