If we are talking about Greek: the Greek article does not have a vocative form and a vocative noun never takes an article either in the classical or in post-classical language. “ὁ κύριε” is simply wrong. However, if a vocative noun is followed by another noun in apposition then the second noun can be in the vocative (as in Matt 11:25 // Luke 10:21: πάτερ, κύριε τοῦ οὐρανοῦ), or it can be in the nominative, with the article (as in Rev. 15:3: κύριε ὁ θεὸς ὁ παντοκράτωρ). Both examples have been quoted in a previous answer. The logic behind this is that a vocative noun is determined by nature, even though it does not take an article. This is a Greek phenomenon and has nothing to do with Aramaic.
ʼabbā “father” is Aramaic, or (with its geminated -bb- ) more precisely: Western Aramaic. It is formally the determined state of ʼaḇ, but it is used idiomatically as a form for addressing one’s own father. Thus, cross-linguistically ʼabbā (determined state) is equivalent to πάτερ (vocative).
More information here: http://cal.huc.edu/ put )b in the search box.