It seems that this means different thing in American English than in UK. Is this true? In British English, "he is not half lucky" means "he is very lucky". In "Lord of the Flies" by Golding, one boy says to another, "You can't half swim", meaning "You can swim very well".
But according to Random House Unabridged Dictionary, "not half" means "not at all, not really" (His first attempts at painting are not half bad—meaning they are not bad at all).