The first "Life" is brought out, a Pythagorean.
τίνα πρῶτον ἐθέλεις παραγάγωμεν: "which one do you want us to lead in first?" παραγάγωμεν is deliberative subjunctive (S. 1805). On occasion, an indicative form of βούλομαι or, as here, ἐθέλω will appear before the deliberative subjunctive (S. 1806; see ἐθέλω LSJ I.A.7). This is a compression of two questions into one (for more, see S. 1806).
τουτονί: "this here." The deictic iota at the end of the demonstrative adds emphasis and immediacy (S. 333g).
τὸν ’Ιωνικόν: "the Ionian." Lucian is a bit unclear about the exact identity of these characters who defend and explain various philosophies. The first philosopher for sale is here described as Ionian and so could be Pythagoras himself, but then he is called a "Pythagorean." As the interview goes on, it becomes apparent from additional biographical details that this character is either a living embodiment of Pythagorean philosophy, or perhaps a hybrid of both the philosopher and his ideas. Lucian is playing with the potentially scandalous idea of auctioning off famous philosophers, but also seems to back away from it by having the characters turn out to be followers of less import. The mention of Ionia connects the character with the reputation of Ionia as a place of learning and philosophy. It also points to the dialect of Greek that Pythagoras spoke, as he spent his early years on the island of Samos, which was considered part of the region of Ionia. See Beaupère ad loc. for more on why Lucian uses this adjective here. There are Ionic features in the Greek of the Pythagorean (uncontracted verbs, nom. sg. -ιη instead of -ια).
οὗτος ὁ Πυθαγορικός: "you there, Pythagorean!" οὗτος is commonly used as a casual form of address (S. 1288a) and for the nominative (ὁ Πυθαγορικός) used in exclamations instead of the vocative, see S. 1288.
κατάβηθι: imperative 2nd sing. aor. active > καταβαίνω. Some verbs have second aorists that are lacking the thematic vowel and so resemble second aorists of -μι-verbs (e.g., στῆθι). γιγνώσκω is another commonly occurring verb with this sort of second aorist (aor. act. imper. γνῶθι). See S. 681, 684, 687 (which has a list of such verbs). Imperative 2nd sing. aor. active > καταβαίνω. This is the regular ending in many aorist imperatives, such as στῆθι, γνῶθι, ἴθι.
κήρυττε: > κηρύσσω, “proclaim or advertise for sale” (LSJ III.1). Attic uses -ττ- where Ionic and most other dialects tend to have -σσ- (S. 78).
πάρεχε σεαυτὸν ἀναθεωρεῖσθαι: "present yourself to be examined carefully." παρέχω can mean "present or offer (for a purpose)" and governs an infinitive that specifies the purpose (παρέχω LSJ A.II; see S. 2008 for the infinitive of purpose).
συνειλεγμένοις: perfect passive participle (> συλλέγω), here used as a dative of agent (S. 1488). It is unusual for the dative of agent to be used in conjunction with verbs of any tense other than perfect or pluperfect (see S. 1490).
ὑπὲρ ἄνθρωπον: super-human, beyond human.
τὴν τοῦ παντὸς ἁρμονίαν: "the order/agreement of everything," perhaps a reference to the harmony of the spheres, a Pythagorean idea about a cosmic correspondence between musical intervals and the movements of celestial bodies. Given that Pythagoras apparently didn't write anything down and there were waves of Pythagorean thinkers over a broad span of time, it is difficult to pin down exactly what Pythagoras actually thought and discussed in his own lifetime. In the discussion that follows, Lucian draws upon a wide variety of ideas attributed to Pythagoras and his followers.
ἀναβιῶναι: aor. 2 infin. act. > ἀναβιόω, come to life again, return to life. This is one of the -ω verbs that has a second aorist in the manner of -μι verbs (ἀνεβίων; see S. 681 and 687). The placement of the accent is due to the fact that Greek infinitives always accent the syllable before -ναι. The infinitive is here parallel with εἰδέναι and both rely on an implied βούλεται supplied from the previous sentence.
τὸ μὲν εἶδος: accusative of respect (S. 1601b).
τί δὲ μάλιστα οἶδεν: "What does he know especially?” i.e. “What is his specialty?"
ἄκρον: > ἄκρος -α, -ον: highest in its kind, consummate (LSJ III).
ἔξεστι(ν): it is allowed, it is possible (+infin.).