Update 4 January 2018 the CJEU held late December and confirmed the functional approach at 53 juncto 57.
I was delighted to learn something I had not been aware of in Szpunar AG’s Opinion in C-467/16 Brigitte Schlömp: namely the slightly diverging approach to the notion of ‘court’ in Brussels cq Lugano.
The AG also opines on the question of lis alibi pendens, suggesting (at 48) that since the conciliation procedure before the Behörd constitutes an integral part of proceedings before a(n) (ordinary) court, the moment of seizure of the Schlichtungsbehörde is the determining moment under the lis alibi pendens provisions of Articles 27 and 30 of the Lugano II Convention. [He also refers to  EWHC 2782 (Ch) Lehman Brothers Finance AG v Klaus Tschira Stiftung GmbH & Anor which followed the same approach].
Is the Swiss ‘Schlichtungsbehörde’ or conciliation authority, intervening in disputes between local councils and relatives with respect to maintenance and social care payments, a ‘court’ under Lugano?
Ms Schlömp, who resides in Switzerland, is the daughter of Ms H.S., who receives supplementary social assistance from the Landratsamt Schwäbisch Hall (administrative authority of the district of Schwäbisch Hall) in Germany because of her care requirements. Under German law (indeed similarly in many a Member State), benefits handed out by social welfare bodies, are claim back from children of recipients, subject to ability to pay. To assert its claim for recovery, the German welfare body lodged an application for conciliation in regard to Ms Schlömp with the conciliation authority (‘Schlichtungsbehörde’), competent under Swiss law. What follows is a series of procedures left, right, even centre. Their exact order is outlined by the AG, they matter less for this post: what is relevant to my own insight, is whether a Schlichtungsbehörde under Swiss law is covered by the term ‘court’ within the scope of Articles 27 and 30 of the Lugano II Convention.
Here comes my moment of surprise: at 58: ‘the concept of ‘court’ in the Lugano II Convention differs from that in Regulations No 44/2001 and No 1215/2012, as that Convention contains an article which has no parallel in the latter two instruments: Article 62 of the Lugano II Convention states that the expression ‘court’ is to include any authorities designated by a State bound by that convention as having jurisdiction in the matters falling within the scope of that convention.’ Like in recent case-law under the Brussels I Recast, bodies which prima facie are outside the judicial system, may be considered ‘courts’. A confirmation of the functional as opposed to the formal classification approach.
(Handbook of) EU private international law, 2nd ed. 2016, Chapter 2, Heading 126.96.36.199.1.