Heart
Due to the strange action of Lenalee's Innocence saving the conformer without her command, Lenalee is suspected to be a possessor of the "Heart". Same goes to Allen, whose heart was eaten through—literally—by Tyki Mikk's Tease. He should have not survived either, but a piece of his Innocence (which was destroyed by Tyki Mikk). So what is this "Heart"?
A Heart is said to be the core of Innocence. It is where all Innocence originated, and where it will all return. This piece is missing at the moment, and both the Order and the Earl are searching for it. However, nobody knows what the nature of the “Heart” is, how it looks like, where it might be located, and where to start looking for it.
That said, there should be one and only Heart whose conformer nobody is sure of, but there are already two strong nominees for the possessor: Allen Walker and Lenalee Lee. I personally don't want that to happen, because that would be boring. We need more things to surprise and amuse us. Things will be much better that way. However, the clues are somehow leading my thoughts to them. *in denial* Here's some more points I put some thoughts into, aside from the whole Innocence-saving-the-conformers thing mentioned above.
unstable vs. more stable
When Allen's Innocence was crushed by Tyki Mikk, he mentioned:
"If Suman's Innocence destroys itself when I demolish your Innocence... Then it means that yours was the "Heart", boy." — Tyki Mikk, chapter 56
But Suman's Innocence didn't, and it was concluded that Allen's Innocence was not the Heart.
Later, after Allen is taken to the Order's Asia branch and finally able to invoke his Innocence again—his Innocence this time holds more strength and different design—Bak Chan analyzes that his Innocence from earlier was just like a less-stable version of the new one. I think it is possible if the improved Innocence was the Heart. Think of the old one as a caterpillar, and the improved one as a butterfly. If it weren't learned in Biology, no one would have thought that a caterpillar would metamorphose into something beautiful. That said, it is possible that the Heart hides itself until it decides that the time has come.
The same argument also applies to Lenalee and the evolution of her Innocence, except that hers was never destroyed, it was simply too weak after the maximum invocation, thus had low synchronicity. So we can't be sure that hers is not the Heart. Well, if you don't believe in my assumption about Allen's Innocence earlier, then Lenalee has more chance of being the possessor of the Heart than he does.
what's in a name?
If the name "Heart" is analogied with one's heart, minds, feelings, or emotions, then it even fits those candidates more. Either Allen or Lenalee fights as an exorcist for no selfish reasons. Lenalee fights for the sake of protecting her world that consists of her brother, her comrades and everyone she holds dear. Allen, on the other hand, fights in order to save both humans and akuma. They're both the type of person who thinks of other people first, and wouldn't really care about the consequences they will face as much as saving the others.
external
There's also another interesting point regarding Allen and Lenalee's probability of being the Heart possessor explained by Janice in her shrine to Allen Walker. Please pay her a visit! :D