Tesla Motors Inc. filed a federal lawsuit against a German auto parts maker for allegedly misrepresenting its ability to design the signature “falcon wing” doors on its Model X electric sport-utility vehicle, leading to a last-minute change to a new supplier that caused delays.

The lawsuit, filed in the U.S. District Court of Northern California, aims to stop the supplier, Hoerbiger Automotive Comfort Systems LLC, from demanding more payment from Tesla after the electric-vehicle maker cut ties with the supplier in May 2015....