In a book (author long forgotten; an Anglican I recall) I read long years past, this arresting phrase "every man in his liturgy" cropped up; come to think of it, it may even have been the title of the book or chapter or whatever.
Dix mentions this in the first page of his magnum opus, since it is in fact a more or less literal quotation from the first Epistle of Pope St Clement I to the Corinthians (one of the first Christian documents surviving apart from the New Testament itself, dated to about 96 A.D., and in early times accorded well-nigh canonical status), which he cites to prove his contention that the sacred liturgy is the corporate act and work of the whole church assembled to obey the Lord's command "Do this in memory of Me".
I was reminded of this by starting to read a collection of Pope Benedict's General Audiences on the Fathers of the Church - here is his first talk on Pope St Clement I (7th March 2007), which has the relevant passage in it.
Here is that relevant passage (I Clement xl, 5 - xli, 1) with Dix's rendering of it, putting in a line break at the chapter division, and adding in square brackets the three words he omitted, plus another literal rendering:
τῷ γὰρ ἀρχιερεῖ ἴδιαι λειτουργίαι δεδομέναι εἰσίν, καὶ τοῖς ἱερεῦσιν ἴδιος ὁ τόπος προστέτακται, καὶ Λευΐταις ἴδιαι διακονίαι ἐπίκεινται· ὁ λαϊκὸς ἄνθρωπος τοῖς λαϊκοῖς προστάγμασιν δέδεται.Ἕκαστος ἡμῶν, ἀδελφοί ἐν τῷ ἰδίῳ τάγματι εὐ[χ]αριστείτω τῷ θεῷ ἐν ἀγαθῇ συνειδήσει ὑπάρχων, μὴ παρεκβαίνων τὸν ὡρισμένον τῆς λειτουργίας αὐτοῦ κανόνα, ἐν σεμνότητι.'[For] Unto the high-priest ( = the celebrant-bishop) his special "liturgies" have been appointed, and to the priests ( = presbyters) their special place is assigned, and on the levites ( = deacons) their special "deaconings" are imposed; the layman is bound by the ordinances for the laity.Let each of you, brethren, make eucharist to God according to his own order, keeping a good conscience and not transgressing the appointed rule ["canon"] of his "liturgy" [, in seriousness].'
Note then that the Church, when she is assembled in the Lord to celebrate His great Act - when, that is, she is most herself and most perfectly in action - is active as a precisely ordered hierarchical organism, each order fulfilling its own liturgy, that the liturgy of the whole be perfectly carried out, and not transgressing the appointed rule. Dix goes on to say, on the second page of The Shape of the Liturgy, that seminal work, that:
...the eucharist [sic] is emphatically a corporate action of the whole christian [sic] body, in which every 'order' from the layman to the bishop has its own special 'liturgy'…
and that (in footnote 1 on page 2):
The laity are an 'order' in the church [sic] no less than the 'holy orders' of the clergy, and were anciently required to undergo a three years' preparation and training before they were allowed to enter it by baptism and confirmation. …
All this remains my settled understanding of my own part in the sacred liturgy, the divine service: we should each fulfil our own liturgy, and not be restlessly pushing into another's part as if we were some frustrated actor forced to play a minor character when we really wished we were the lead...
I often think of this when singing or serving or simply hearing Mass: the priest is fulfilling his part, and I must fulfil mine; that is why I don't always feel the need to slavishly attempt following every word mystically uttered, for I know that the mystery of our redemption is being made present, and to dispose my heart (so cold, so divided) to receive the secret operation of grace brought to us in the Sacrifice and Sacrament is the most important thing, "the one thing necessary".
I pair this thought with what the great mediæval canonist Lyndwood wrote about why the Canon (significant word, that) is said so quietly by the priest (fulfilling his liturgy): Ne impediatur populus orare, that the people be not impeded from praying (and so fulfilling their rightful role).