It is writing about the DMV, the government agency that issues driving licences in the USA. The experience that many people have of the DMV is that it is slow, and inefficient. The author is making the point that the democratic control that we should have over the DMV doesn't seem to work.
Now to consider the phrase - it is using metaphor. "Lurch" means to move in an uncontrolled manner. "Sideways" suggests it is not making progress. "of its own inertia": Inertia is the tendency of things to maintain speed and direction, unless forced to change. The word "of" here indicates a "cause or origin": compare "he died of cancer" (cancer was the cause of his death) with "it lurches sideways of its own inertia" (its own inertia is the cause of it lurching sideways)
So the DMV doesn't make progress (in customer service) Instead the same failed ideas get recycled. Reforms don't result in improvements as there is no effective oversight or control.
It's pretty critical of the agency: I don't know how accurate this is (since the system is different in the UK)