Excuse me for necro-posting, but the declension of nouns in the second line here made me suspicious and I turned to the dictionary. Allen and Greenough's New Latin Grammar (1903) entry on the dative of possession* (para. 373, pp. 232-233, online at https://dcc.dickinson.edu/grammar/latin/dative-possession) states that it is the one for whose sake something exists that is in the dative, e.g. Est mihi domī pater (Ecl. 3.33) -> I (dat.) have a father (nom.) at home, literally there is for me at home a father; est mihi liber -> I (dat.) have a book (nom.) EY's English meaning comes out as "neque domini defensor", whereas "neque defensori dominus" translates back to English as "no champion hath a lord".
* not really possession, as it expresses the idea of something that is there for the benefit of something else, like the Classical Chinese coverb 為.
I suppose that is a possible reading, but in my opinion a most unnatural one. Compare: "No dog has the home". This can technically be parsed as "the home [a specific home I'm talking about] has no dog", but this would be a very weird word order in English. Furthermore, if one is making a simple general statement, which is one reading of the OP verse, one is by that token not talking of a specific something, so one does not expect a definite article: "No dog has a home" or "No home has a dog". "The" would be warranted in a didactic or normative text, e.g. "The [good] home has no dog" or "The [good] home shall have no dog," and in fact reverting the OP verse to normal word order - "The rescuer has no rescuer / The champion has no lord" - enables one to read it as a didactic statement (which seems reasonable), but inverting the word order renders such sentences unintelligible. In fact, the prior probability of the definite article in that position of the OP verse is so low that it only really registered on my mind after I read your comment. Word order in English is so strict that I was always perceiving it as "No rescuer has a rescuer / no lord has a champion", and I suspect I am not the only one. You yourself used the indefinite article in your rewording!