Based on the manga, I think Allen is the person who possessed the cœur, coeur as the Cardinal did mentioned that his existence is to protect the " heart"
In my own, I think it's Allen Walker who has the "Heart" because not only is he exceptional but he became a point breaker in the age of 15. Lenalee is a different case cause komui a dit that any equip type can be crytal type/ parasitic. so to point it out, maybe his arm being a sword/equip type is so unnatural. so He is the Heart!!!
I really think that Allen contains the heart. At first I thought that Lenalee ou Lavi contained the cœur, coeur but, Allen was the main character, it is plus sensible that he contains the heart.
