This sounds like a very interesting project with some real applications. Water should work well to remove lye, as it is water-soluble. You won’t be able to remove every trace of lye, so you will need to research how much lye would be acceptable in drinking water. You should be able to detect lye based on pH. Any water that contains lye will have an elevated pH. You can measure the changes in pH using a pH meter or pH test strips. pH test strips will be the cheaper and easier way to go. You will probably be able to find some from one of the approved suppliers:
https://www.sciencebuddies.org/science- ... lies.shtml
Lye is a hazardous chemical that can cause severe chemical burns. It also creates a lot of heat when added to water. When mixed with certain metals lye can produce hydrogen gas, which is explosive. There is more information about the chemical properties of lye here:
http://cartwright.chem.ox.ac.uk/hsci/ch ... oxide.html
and here:
https://www.sciencebuddies.org/science- ... lies.shtml
You will need to make sure that you get approval to use lye. Most science fairs place restrictions on the use of hazardous chemicals and require pre-approval. Ask you teacher what you need to do to meet all the requirements.
If you do decide to use lye make sure to get the correct personal protective equipment. You will want a lab coat, goggles, and special gloves. You will probably want to use the chemicals inside a fume hood for added safety. More information on chemical safety can be found here:
https://www.sciencebuddies.org/science- ... fety.shtml
And make sure to dispose of your chemicals properly. In some places small amounts of dilute solutions can be flushed down the sink with large amounts of water. Larger amounts of lye must be neutralized with acid before disposal. Your teacher should help you with the handling and disposal of these chemicals.
How are you going to make the activated carbon? From my short Google search it would seem that the chemical activation is followed by high temperature treatment (450-900 degrees C according to Wikipedia).
Let me know if you have any more questions.
-microkts