Yeah, it was her friend's grave. Although it was supposed to be hers.

She 'experienced' her own death and then somehow the grave belonged to someone else. She was so certain she actually died that she was desperate to see that gravestone. I'd say it was a pretty serious mindsmurf for her. I don't know the intricacies of it all, though... I should really read through the DataLogs sometime. xD My understanding of it is that she was supposed to die, but because Etro saved the heroes of FFXIII from eternal crystal sleep, time changed and her friend died instead.

She basically is a paradox, I guess... which I can only imagine means that if Noel and Serah are out correcting time, then she would need to be 'corrected' as well, perhaps? I think we'll see more of her in the almost inevitable FFXIII-3.