Ponyboy says this in reference to his thought that his older brother Darry does not love him. He says,
Darry thought I was just another mouth to feed and somebody to holler at. Darry love me? … I don't care, I lied to myself, I don't care about him either.
What Ponyboy means when he says that he lies to himself all the time is that he deludes himself. He suppresses thoughts that are too difficult to contemplate, such as the emotional distance he perceives as existing between himself and Darry. By saying that he does not care about Darry in response to his view that Darry does not love him, he is not being truthful with himself or with the reader. If he were honest, he would admit to himself that Darry and Soda, his two brothers, are the most important people on earth to him since his parents...
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were killed in a car accident. He acknowledges to himself that he loves Soda. This is fairly easy for him to admit because Soda is more emotional and demonstrates how much he loves Ponyboy. Darry, on the other hand, appears unemotional and unreachable. He never shows Ponyboy any warmth or emotion that would indicate that he loves his younger brother. Ponyboy therefore believes that Darry does not love him.
Ponyboy is very hurt by this but tries to suppress his feelings about his brother and his unhappiness that Darry seemingly does not love him. By telling himself that he doesn't care about Darry, just as Darry doesn't care about him, Ponyboy is lying to himself.
Soda's enough, and I'd have him until I got out of school. I don't care about Darry. But I was still lying and I knew it. I lie to myself all the time. But I never believe me.
It becomes clear by the end of the novel how much the three brothers love one another and how much Darry's love means to Ponyboy.
The death of Ponyboy's parents was a traumatic experience for him, just as it would be for any 14 year old. Ponyboy has problems dealing with the new head of the household, his 20 year old brother, Darry. Darry works all the time, having given up his chance at a college football scholarship in order to support the family. Darry takes his responsibility seriously, since he knows his two younger brothers may be placed in a foster home if things go wrong. Consequently, Darry keeps a tight rein on Pony, who he knows has a bright future ahead of him (unlike Soda, who has already dropped out of school). Pony tries to convince himself that he hates Darry, and that Darry hates him. Soda tells him that it is not true, but Pony is never quite sure. Pony's guilt concerning this relationship hounds him throughout the novel.
Following Johnny's death, Pony tries to convince himself that it was he, and not Johnny, who had killed the Soc in the park. This comes in part because Pony has suffered a concussion and is not thinking clearly, but it is primarily because he blames himself for all of the problems--Johnny killing the Soc, the church fire, and for Johnny's critical injuries. Johnny was Pony's best friend, and Pony tries to keep Johnny's memory alive by trying to remember only the good things he had shared with him.