Sensitive test for lead in water? Some of my friends are in Flint and I'm horrified by their situation. I would like to learn how to test for lead independently. 

After all if you can't trust the state sending them water to test is not sufficient. The testing procedures I have read about give too many type II errors. A procedure with a bias toward type I errors would be better since then I could pay a professional lab to see if it was real.

For tests that only detect high levels of lead, could they be made more sensitive by evaporating the water then testing a larger sample?
I used to work in an environmental water testing laboratory.  The regulatory standard method for testing for lead in water uses an Atomic Absorption (AA) spectrophotometer.

It seems that the issue with Flint's water appears to be that the new source of water is corrosive, the water has not been treated for corrosion, and pipes in Flint are commonly made out of lead.  So if your pipes at home are made of lead and are corroding, you may have a problem that the lab at the water treatment plant was not able to test for.

If you are curious about checking your water at home, you can obtain a water testing kit from a local hardware store.  These kits come with test strips that allow you to check your water for things like nitrates, pH, alkalinity, hardness etc.  Make sure your kit allows you to test for lead.