NOTE: this question contains major spoilers for Lolita.
When we first meet Humbert he's awaiting trial for murder and in the fullness of time, it becomes explicit exactly who it is that he has murdered. However, there does seem to be limited evidence that he's committed another murder in the course of the book and decided to skip over it, the unreliable narrator of his own story that he is.
The death in question is that of Charlotte Haze, Lolita's mother. Charlotte marries Humbert and he fantasies about murdering her to gain unfettered access to abuse her daughter:
The natural solution was to destroy Mrs. Humbert. But how?
He decides against it, simply due to the likelihood of his being caught. She later reads Humbert's diary, discovers his abhorrent lust for her daughter, and decides to move them both away from Humbert's attentions. Before she can do so she is killed in what seems to be a freak car accident.
However, there are two clues, late in the novel, to suggest this may not be so accidental after all. First, teenage Lolita herself suggests (remember this is Humbert's narration of her words) that she was killed deliberately:
"Where is she buried anyway?"
"Oh, you know, my murdered mummy."
Humbert does not correct her on this implication. Shortly afterwards Humbert is describing the murder of another woman, killed by her husband who was caught and tried. He then says:
I did better.
In some respects, these feel like an open and shut case of admission of guilt. However, against this, there's a big question of how Humbert might have arranged the murder. There are a number of eyewitnesses to whom the death appears to be a straightforward accident. The police accept it as accidental. There is no suggestion that the person driving - a Mr. Frederick Beale, Jr - was known to Humbert. Beale later visits Humbert, professes his innocence and offers to pay the funeral expenses. This could, of course, be made up on Humbert's part but his style of lying through the rest of the book is more to let slip telling details rather than outright fabrications.
How, then, are we to reconcile the apparent admission of guilt by Humbert for Charlotte's murder with the apparent lack of means for orchestrating it?