Who is that person Kanda Yu is looking for in D.Gray-Man?

Answer 1

No one is certain who 'that person' is many popular theories are:

1) that 'that person' is actually related to the Lotus Flower which in turn is what represents Kanda's life span.

2) another popular theory seems to be that 'that person' does not even exist and is simply just a way of Kanda's 'coping'

3) 'that person' is connected to the Lotus Flower, and is not Kanda's life span, but someone Else's.

4) That the Lotus was actually a power possessed by the Noah Family or a neutral figure that we are left to see, whom Kanda could be searching for in order to ask why they left the Lotus in his care, and to see their motives.

5) That the Lotus itself is what keeps Kanda alive, and also implying that 'that person' does not actually exist, but more or less, Kanda's way of explaining his actions and thoughts.

6) another popular theory is that the person whom Kanda is searching for is actually an older/younger sibling,

7) and the final theory i can find is that the when the Lotus dies, Kanda will too, but as stated in episodes 34 and 35 it will re-awaken in 1000 years, and Kanda will come back to life in order to fight again, if that would even be necessary.

Im sure there are many more speculations based on stuff that has been hinted at in the manga/anime. All of these are simply speculations and opinions, which one you believe in is your choice. Hopefully we will soon receive some clues or the full story from the creator of D Gray Man. Hope this was a bit of help.