Advocate-General Bot opined on 6 September in C-386/17 Liberato. (Not as yet available in English). The case is slightly complicated by the application of not just former Regulation 44/2001 (Brussels I) but indeed a jurisdictional rule in it (5(2)) on maintenance obligations, which even in Brussels I had been scrapped following the introduction of the Brussels IIa Regulation.
The Opinion is perhaps slightly more lengthy than warranted. Given both the Brussels I and now the Brussels I Recast specific provisions on refusal of recognition and enforcement, it is no surprise that the AG should advise that a wong application by a court of a Member State (here: Romania) of the lis alibi pendens rules, does not justify refusal of recognition by other courts in the EU: the lis alibi pendens rules do not feature in the very limited list of possible reasons for refusal (which at the jurisdictional level lists only the protected categories, and the exclusive jurisdictional rules of Article 24), and it was already clear that misapplication of jurisdictional rules do not qualify for the ordre public exception.
It would not hurt having the CJEU confirm same.
(Handbook of) EU Private International Law, 2nd ed. 2016, Chapter 2, Heading 188.8.131.52.3, 184.108.40.206.4.