Article 34 Brussels Ia reads that it applies when “an action is pending before a court of a third state at the time when a court in a Member State is seised of an action which is related to the action in the court of a third State”. In BB Energy (Gulf) DMCC v Al Amoudi & Ors  EWHC 2595 (Comm) Baker J expressed obiter and most cautious views on what I suspect will be one of the points of discussion of Article 34, namely whether ‘pending’ means that the court of the third State was first seised, or simply that at the time of the application, there are two sets of proceedings.
At 23 Baker J said that ‘Articles 33 and 34 “do not seem to replicate the primacy of first seisin built into Articles 29 and 30.” However he did not engage at any length at all with the A33-34 conditions, for [at 15] ‘It is, however, common ground that Article 34 of the Brussels Regulation (recast) does not apply because the Moroccan proceedings are in the nature of insolvency proceedings excluded from the scope of the regulation.’
His views on the A33-34 conditions are put in the most cautious of terms: at 23: ‘Articles 33 and 34 appear to include requirements not found in Articles 29 and 30, but on the other hand they do not seem to replicate the primacy of first seisin built into Articles 29 and 30.’ (emphasis added)
There is convincing argument in my view that A34 does include a condition of the non-EU court having to be seized first.
(Handbook of) European Private International Law – 2nd ed. 2016, Chapter 2, Heading 188.8.131.52