There are test strips for lead testing water, but they're unreliable, unregulated, and not particularly trustworthy. The only great option right now is to call a lab who does water testing and work with them to send in a sample and have it tested via a method like induced plasma mass spectrometry.
Unfortunately many of these labs aren't interested in working with individuals who will only send one or two samples. They prefer to work with companies that will send them hundreds of thousands of samples. Even if you found one willing to work with you, their business processes involve fax machines, invoices, and talking to sales people on the phone.
(Related: That's why I started a company called http://www.testyourwaterforlead.com. We started a company and partnered with a lab, we let you order online, pay with a credit card, and we deal with the lab to help you avoid the hassle.)