Have a look at this open source project:
http://www.easyracelaptimer.com/

It's from the FPV Racing guys. Basically it uses Infrared Transponders and the software runs on a Raspberry PI. Configuration and monitoring is done using the webbrowser and a local wifi network provided by the Raspberry PI.

I already built a system, however I didn't test it yet at the track. This will be done this weekend. Dry tests on the work bench seem promising. There's even supposed to be an app that announces lap times for you.

I'll tell you how well that system works. At least it's not that expensive.

Andreas