Whatever the doctrinal import, the meaning of the language is something that can be considered by referencing usage elsewhere. The LSJ specifically calls this out as not an example of ἡλικία.V “stature”. Here is the stature section.
V. of the body, stature, as a sign of age, Hdt. 3.16, Pl.Euthd.271b, D.40.56; τῇ ἡ. μικρός Ev.Luc.19.3 (but προσθεῖναι ἐπὶ τὴν ἡ. πῆχυν ἕνα add a cubit to one’s age (cf. πήχυιος), Ev.Matt.6.27); ἄνδρας ἡμισταδιαίους τὰς ἡ. Luc.VH1.40; height of a pillar, Id.Syr.D.28.
That the word ἡλικία could ever mean “stature” was strange to me, but here are the examples, all clearly referring to size somehow.
Hdt. 3.16 ὡς μέντοι Αἰγύπτιοι λέγουσι, οὐκ Ἄμασις ἦν ὁ ταῦτα παθών, ἀλλὰ ἄλλος τις τῶν Αἰγυπτίων ἔχων τὴν αὐτὴν ἡλικίην Ἀμάσι, τῷ λυμαινόμενοι Πέρσαι ἐδόκεον Ἀμάσι λυμαίνεσθαι.
Pl.Euthd.271b ΚΡ. Ὃν μὲν ἐγὼ λέγω, ἐκ δεξιᾶς τρίτος ἀπὸ σοῦ καθῆστο· ἐν μέσῳ δ’ ὑμῶν τὸ Ἀξιόχου μειράκιον ἦν. καὶ μάλα πολύ, ὦ Σώκρατες, ἐπιδεδωκέναι μοι ἔδοξεν, καὶ τοῦ ἡμετέρου οὐ πολύ τι τὴν ἡλικίαν διαφέρειν Κριτοβούλου. ἀλλ’ ἐκεῖνος μὲν σκληφρός, οὗτος δὲ προφερὴς καὶ καλὸς καὶ ἀγαθὸς τὴν ὄψιν.
D.40.56 καὶ ἐγὼ μέν, ἐάν, ὃ μὴ γένοιτο, ὑμεῖς με ἐγκαταλίπητε, οὐχ ἕξω ὁπόθεν προῖκα ἐπιδῶ τῇ θυγατρί, ἧς τῇ μὲν φύσει πατήρ εἰμι, τὴν δ’ ἡλικίαν αὐτῆς εἰ ἴδοιτε, οὐκ ἂν θυγατέρα μου ἀλλ’ ἀδελφὴν εἶναι αὐτὴν νομίσαιτε·
Ev.Luc.19.3 καὶ ἰδοὺ ἀνὴρ ὀνόματι καλούμενος Ζακχαῖος, καὶ αὐτὸς ἦν ἀρχιτελώνης καὶ αὐτὸς πλούσιος. καὶ ἐζήτει ἰδεῖν τὸν Ἰησοῦν τίς ἐστιν, καὶ οὐκ ἠδύνατο ἀπὸ τοῦ ὄχλου ὅτι τῇ ἡλικίᾳ μικρὸς ἦν.
Luc.VH1.40 τῷ δ’ ἐνάτῳ μηνὶ πέμπτῃ ἱσταμένου, περὶ τὴν δευτέραν τοῦ στόματος ἄνοιξιν—ἅπαξ γὰρ δὴ τοῦτο κατὰ τὴν ὥραν ἑκάστην ἐποίει τὸ κῆτος, ὥστε ἡμᾶς πρὸς τὰς ἀνοίξεις τεκμαίρεσθαι τὰς ὥρας—περὶ οὖν τὴν δευτέραν, ὥσπερ ἔφην, ἄνοιξιν, ἄφνω βοή τε πολλὴ καὶ θόρυβος ἠκούετο καὶ ὥσπερ κελεύσματα καὶ εἰρεσίαι· ταραχθέντες οὖν ἀνειρπύσαμεν ἐπ’ αὐτὸ τὸ στόμα τοῦ θηρίου καὶ στάντες ἐνδοτέρω τῶν ὀδόντων καθεωρῶμεν ἁπάντων ὧν ἐγὼ εἶδον θεαμάτων παραδοξότατον, ἄνδρας μεγάλους, ὅσον ἡμισταδιαίους τὰς ἡλικίας, ἐπὶ νήσων μεγάλων προσπλέοντας ὥσπερ ἐπὶ τριήρων.
Id.Syr.D.28 τὰ δὲ προπύλαια τοῦ ἱροῦ ἐς ἄνεμον βορέην ἀποκέκρινται, μέγαθος ὅσον τε ἑκατὸν ὀργυιέων. ἐν τούτοισι τοῖσι προπυλαίοισι καὶ οἱ φαλλοὶ ἑστᾶσι τοὺς Διόνυσος ἐστήσατο, ἡλικίην καὶ οἵδε τριηκοσίων ὀργυιέων.
First, from reading these, it seems clear that the idea for most of these is similar to our expression of “at full growth”, etc. It’s a statement about size and age at the same time, with size as a function of the age, just as the LSJ has it.
The Plato and Demosthenes examples seem to express the “stature as growth” idea very clearly to me, and are both in reference to a young person. The Herodotus, Luke, and first Lucian example all concern someone of abnormal growth, very tall, or very short. I assume that the last is meant to invoke the idea of a giant erection. (I see that J.L. Lightfoot suggests the same.)
So I think that the LSJ citation is correct for Matthew 6:27. He is not speaking to teenagers or to a short male support group, and so ἡλικία refers to “age”, not “growth” or “stature”.