Lan, raised together with her brother by a friend of her father's, has learnt responsibility early, assisted by being the woman in a household of men in a society that expects women to be the chatelaines of the house and do all work thereto, and by having a dearly loved little brother (enough said). The fact that she possesses psychic powers which she must control has doubtless led to this as well; had her guardian Kiryuu Jin not drummed it into her head, she could have been fearfully destructive.
Many of her powers seem to be growing with the (late) onset of puberty, and made to grow by their forced use. Lan's use of her esper abilities is reflexive and usually unconscious, and has been so for long enough that she seems to believe they will always be so. However, her survival reflex is ingrained enough that she uses the powers to save herself from the "accidents" Sonnet engineers; and each time she pulls more power, more seems to be left to her thereafter. (In other words, every time she has to go beyond her limits, they aren't limits any more.)
The power lies in her blood (literally; she has a unique blood chemistry that apparently contains Esper retrovirii) and the keys to its use are locked in her head. It seems to me that most of the time Lan is actually unconciously suppressing her power, in order to avoid being thought any odder than she might.
But Lan is not who she thinks she is, and in all probability bears none of the blood of her father at all. From Dr. Mericus' speech, it seems that she was created in a lab to be as much an Ancient as possible, and from her hidden memories it seems that she was raised by wolves for a time after that. How she came from there to Kiryuu I do not know.
As an Esper, she has natural psychic talents of unparalleled magnitude, and has used them both to save herself and to save others. And, moreover, she has the ability to touch the Akai Kiba. (Despite Mericus tachi's mistaken beliefs, the Akai Kiba is its own entity rather than some suppressed person within Lan. When it manifests through her, however, it manifests THROUGH her, taking on the appearance of her own true form.)
She seems to be attracted to, and perhaps in love with, Bird. (Although if Wataru repeats his crack about being a cupid of love for the two of them, he is in great danger of being smacked with a wet sponge.) Certainly it was he who called her back from melding fully with the Akai Kiba. I think that the two of them are indeed marked to end up with each other.
Lan has a quiet core of strength which reveals itself under pressure; she manages, somehow, to cope with every emergency with which she is presented. Had she and Sonnet encountered each other under different circumstances, they might well have been the best of friends.
Her seiyuu is Wada Kanda, best known for the voice of Shildy
and Varji/Barje in GallForce.