Matt pretends he doesn't care much about L. He knows that if he begins demonstrating any interest in their shared predecessor, Mello will feel threatened by the possibility that Matt may also aspire to succeed L, so Matt doesn't really bother mentioning it at all.
However, he is intrigued by the ghost that haunts Wammy’s, a stranger that the children have spent their entire lives reaching out towards. Matt may not have obsessed over grades as he knew Mello had, but his hard work was evident in the fact that he consistently defended his position as the House's Third. There is something paternal, albeit distant, about L; for a boy that never knew his parents, Matt seeks comfort in his own personal idea of the detective.
A quiet man, but one who smiles warmly when he notices you approach. Matt envisions him as a listener, someone to whom you could confess yourself without judgement, but instead recieve a deliberated word of advice. Matt sees accents of himself in L. He wants him to have the same shade of red hair as he does or the scattering of freckles across his nose. He wants L to find it difficult to sit still, to maintain focus. He loves Mello but cannot relate to him in his sharpness, his ability to plan and carry it through without distraction. In L, he sees someone obsessive, yes, but human.
Matt thought that he would be more affected by L's death than he actually was. By this time, the concept of the L had transcended the man himself, and Matt decided to speak to him for the first time in the seclusion of the bedroom he had shared with Mello until he left without saying goodbye. Matt struggled with this, and he wondered what L would do in the shadows of such loneliness.
He asks L, but receives no answer. L is, after all, not a father.