When we were shown the scene of Lucy's body it had various phone voicemails being played. Am I wrong in remembering that Lucy's phone was seen with her body?

No it was just her bag with her make-up fallen out on the ground.

I think the implication was that Lucy was dumped on the Common with her bag, and a person or persons unknown (probably Ben) took the valuable items - her purse and phone - which made the police assume it was a mugging.

This is why her bag was disturbed with the make-up etc spilled out.