DragThing works well on 10.7.3 on my setup. You should contact the author and send him a crash report. The crash reports are stored inside the Library folder which is in your home folder, in Logs/DiagnosticReports. Unfortunately, Apple hides the home Library folder for some reason in Lion, so to get there you'll have to hold down the Option key and choose "Library" from the Go menu. After you do that, navigate to Logs/DiagnosticReports, find the crash report file for DragThing, and e-mail that to the developer, who will then be better able to figure out what's going on.
Also, if you have Application Enhancer, SIMBL, or any InputManager hacks installed, try removing those, as those can often cause crashes and other weird problems in other applications.