Does not keeping a promise violate the precept on lying? What if I promised myself? In my opinion, if you promise something to someone and don't keep it, it is equivalent to lying. But what if the promise is to myself and I don't keep it; is it violating the precept on lying?

Does the lying precept apply to oneself, i.e not lying to yourself?

Sutta / Vinaya references would be very much appreciated.

Edit: I meant one vowed/ promised with honest intention at the time did it, but later change mind and don't want to keep it anymore
In order to answer this sort of question, you have to be clear on what the precepts are and what they are not. They are a set of intentional statements of will to keep a finite set of basic moral precepts. They are not an all-encompassing treatise on morality.

So, the fourth precept, as Sankha Kulathantille says in his answer, relates to a specific type of speech; it does not include all types of wrong speech, it only refers to speech that is intended to deceive another person, as per the Cunda Sutta (AN 10.176) for example:


  There is the case where a certain person engages in false speech. When he has been called to a town meeting, a group meeting, a gathering of his relatives, his guild, or of the royalty [i.e., a royal court proceeding], if he is asked as a witness, 'Come &amp; tell, good man, what you know': If he doesn't know, he says, 'I know.' If he does know, he says, 'I don't know.' If he hasn't seen, he says, 'I have seen.' If he has seen, he says, 'I haven't seen.' Thus he consciously tells lies for his own sake, for the sake of another, or for the sake of a certain reward.
  
  http://www.accesstoinsight.org/tipitaka/an/an10/an10.176.than.html


Therefore, your premise,


  if you promise something to someone and don't keep it, it is equivalent to lying.


is not in accordance with a strict Buddhist understanding of lying, since there need not be at any time during the change of heart an intention to deceive.

As to whether breaking a promise is wrong, Thanissaro has a discussion of this in his BMC:


  The Mahavagga (III.14.1-14) imposes a dukkata on the act of making a promise with pure intentions but later breaking it. Since the texts make no mention of any circumstances beyond one's control that would exempt one from that penalty, a bhikkhu should be very careful of how he states his plans for the future. A special instance of breaking a promise -- accepting an invitation to a meal but then not going -- is treated under Pacittiya 33.


Interestingly, the Mahavagga passage in question does use the word for lying (musāvādā): 


  Nanu mayā, moghapurisa, anekapariyāyena musāvādo garahito, musāvādā veramaṇī pasatthā?
  
  "Has not falsehood been reproved, and abstinence from falsehood been praised by me in many ways?"


But the Buddha only charges him with a dukkata rather than a pacittiya (which would be the case in a true lie), so a distinction is clearly made.

So, first point to make:

Breaking a promise is wrong, but outright lying is worse. Breaking a promise does not, therefore, break the first precept as it is understood in Theravada Buddhism.

Now, on to your question :)

"Lying to oneself" would literally mean knowing something to be false and yet telling yourself that it is true, with the intention that you should believe it to be true. Psychologically, it is certainly possible that over time you could come to convince yourself of something, but only if you let yourself believe it to be true, in which case you would no longer simultaneously know it to be false. This sort of self-deception goes on all the time in our world, of course, but is it lying?

First of all, the five precepts all require physical or verbal acts to be broken; morality in its conventional form always refers only to physical and mental commissions or omissions; mental immorality is considered a lapse of concentration, not morality. (I don't have a reference for this, but if I can find one, I'll pass it along). So you'd have to actually tell yourself out loud, knowing that what you were saying is false, intending to make yourself believe something to be true. I guess that is theoretically possible, but in most cases I think it would be difficult to convince yourself that you were seriously capable of such deception.

More common, I'd say, would be the simple intention to cultivate a belief in what is false; rather than trying to deceive yourself, per se, you simply want to cultivate a distorted belief; e.g. believing that a loved one is still alive, because it's too difficult to acknowledge they are dead. The difference here is there is no breach of trust; you are accepting that something is a lie, but deciding to believe it anyway.

A similar situation would be in the case of hypnosis, where a hypnotist tells the patient to imagine themselves in certain situations, or helps them convince themselves they were never afraid of something, etc., e.g. "You have never been afraid of spiders." The patient allows the hypnotist to make them believe something that is false; the hypnotist cannot be considered guilty of lying to the patient, as the patient knows it is false but simply wants to change their belief.

In short, lying to yourself, while it may be damaging, can't be considered truly lying, since it doesn't involve a breach of trust or an act of deceptive communication. Self-deception is voluntary and occurs after the 'lie' has already been told.