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The most interesting and surprising solution (step 7 below) was given by Steve Herman.
1. (Ax)[Human(x) -> Hates(x,e(lc))]
2. (Ax)[Hates(e(lc),x) <-> (x = lc)]
3. Human(e(lc))
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4. Human(e(lc)) -> Hates(e(lc),e(lc)) A-elim 1
5. Hates(e(lc),e(lc)) -> elim 4,3
6. Hates(e(lc),e(lc)) <-> (e(lc) = lc) A-elim 2
7. e(lc) = lc <-> elim 6,5
8. (Ax)[Human(x) -> Hates(x,lc)] = elim 1,7
Of course, there are some more but less interesting conclusions, e.g. Kim-Jong-un hates Lady Chatterley.
hoodat: That everyone hates Lady Chatterley is not a premise but a conclusion (step 8). The premise is that everyone hates the enemy of Lady Chatterley.
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