I reviewed Bot AG’s Opinion in C-386/17 Liberato here. The Court confirmed last week. Whether lis alibi pendens applies, entails applying jurisdictional rules (in essence an assessment as to whether parties are the same etc.). Except in the very rare cases of (now) Article 45 1(e) Brussels I Recast, infringement of jurisdictional rules does not feature among the reasons for refusal of recognition. Alleged infringement of the lis alibi pendens rule does not therefore qualify as ordre public.
(Handbook of) EU Private International Law, 2nd ed. 2016, Chapter 2, Heading 188.8.131.52.3, 184.108.40.206.4.