why is he not happy
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Because his father is more enamored with heath cliff than his own son. He feels that it is easier to leave rather than stay there and feel like an outsider in his own home.
I know this question was asked a year ago, but I can't leave such an inherently wrong answer loose on the Interwebs.
Nothing is mentioned about Lockwood's father in the entire novel, so I assume the above answerer got confused with which character they were answering the question about.
Lockwood removes himself from London to Thrushcross Grange due to an unfulfilled love affair in London which he is attempting escaping from by making himself "removed from the stir of society", probably because he is feeling sorry for himself.