It could, but on ciebie nie lubi is more natural word order. On nie lubi ciebie would put emphasis on ciebie, meaning that he doesn’t like you, but he likes someone else (me, for example).
As for cię / ciebie, in most contexts they are interchangeable. Most commonly ciebie is used at the beginning of the sentence, while cię in the middle and at the end, but that’s no hard rule.
I have to disagree at the second paragraph. Long forms of pronouns (mnie (as a dative), ciebie, tobie) are used at the beginning, at the end and can be used in middle of the sentence when we give an emphasis on them. "On nie lubi cię" is not correct (though totally understandable) and should be "on nie lubi ciebie".
Otherwise we use the short forms (mi, cię, ci).
However if the pronoun is the second word and the first word is a short conjunction (like a, i, bo, to, więc) we can use both of the forms.
Dear lucas.hbs, I use "Polish Grammar in a Nutshell" by Oscar E. Swan (downloaded free from the internet; very brief and basic) and "Polish, an essential Grammar" by Dana Bielec published by Routledge (very detailed). Between the two of these I get by and can figure out most grammar issues