I think all we've been told is that Lucy died from a blow to the head. A pathologist would be able to pick up signs of each individual injury, the timeline, and also determine which one killed her. They can also tell from skull trauma if a blow was the result of a fall or being deliberately hit over the head.
Presumably, since we've not been told any different, the police can tell the last injury Lucy received was both deliberate and the fatal one. What we've been speculating about is Ian and Jane persuading themselves the fall which caused the blood in the car lot was deliberate and that it killed her (eventually). I don't think the police themselves (even the inept EE police) can be confused about the timeline or which blow killed Lucy.
