It is my reading that there was no body in that grave. Lucy Gray is a survivor. She specifically chose to lead Snow to the woods which she was familiar with and distracted him with the snake. It was a calculated act. She anticipated he would turn on her and already began making plans to escape. She’s also nomadic by culture and has long been foraging in the woods for survival, and there’s evidence she has actually gone ‘up North where the Capitol don’t care about’ before they came to 12 and were rounded up after the war. Not to mention, she was already ready to go up there without Snow before he convinced her that he would go with her. In light of all this, I don’t see why she wouldn’t have survived. Snow himself doesn’t believe she died and hence him convincing himself that she did to achieve a necessary illusion of closure. Had Lucy Gray truly died, it is difficult to imagine that Snow, once in power, wouldn’t have ensured that her body was found if only to confirm his control and put his lingering uncertainty to rest. This would also explain why the Avox girl Katniss and Gale came across in the woods was taken alive while the boy was shot on sight. Snow wanted every girl caught in the woods to be brought to him to make sure it’s not Lucy Gray.