In considering the λαμβάνειν + inf. construction προέλαβεν μυρίσαι, I think it is beneficial to see λαμβάνειν + inf. as a construction. That is to say that the vagueness and conjectural nature of the first part of the BDAG entry is something worth looking into. In considering the only NT verse:
to use this periphrastic construction, I have found it useful to consider the following passage from:Mark 14:8 wrote:Ὃ ἔσχεν αὕτη ἐποίησεν· προέλαβεν μυρίσαι μου τὸ σῶμα εἰς τὸν ἐνταφιασμόν.
The meaning of that is that Tellias killed three birds with one stone.Diodorus Siculus, Library, 13.90.2 wrote:μιᾷ γὰρ πράξει διελάμβανεν ἀφελέσθαι θεῶν ἀσέβειαν, πολεμίων ἁρπαγὰς πολλῶν χρημάτων, μέγιστον ἑαυτοῦ τὴν εἰς τὸ σῶμα ἐσομένην ὕβριν.
In both Mark and Diodorus Siculus the prefixed preposition is used at a syntactical rather than lexical level - ie the meaning of the verb is not changed, but its relationship to the other elements in the narrative is made clear.
If the λαμβάνειν and the λαμβάνειν family of verbs are taken together as verbs of thinking, rather than just several of them are given individual metaphorical senses, then the idea of decision, deciding to do, or "taking it upon oneself" (+ inf.) to do something, is clearly novel, but not much of an extension of the meaning present in the Classical idiom.