Lexical Definition

‎λειτουργέω‎ leitourgéō (li-toorg-eh'-o) to minister ^G:V
from ‎λειτουργός‎

minister.

• to be a public servant, i.e. (by analogy) to perform religious or charitable functions (worship, obey, relieve)

Abbott-Smith

λειτουργέω, -ῶ (< λειτουργός), [in LXX chiefly for שׁרת pi., also for עבד, צבא, etc.;]
1. in cl., at Athens, to supply public offices at one's own cost, render public service to the State, hence, generally,
2. to serve the State, do a service, serve (of service to the Gods, Diod., i, 21): of the official service of priests and Levites (Ex 29:30, Nu 16:9, Si 4:14, I Mac 10:42, al.; cf. Deiss., BS, 140 f.), He 10:11; of Christians: c. dat. pers. seq. ἐν, Ro 15:27 (cf. Si 10:25); τ. κυρίῳ, Ac 13:2.†
SYN.: λατρεύω (q.v.), prop., to serve for hire, LXX (as sometimes in cl.), always of service to the deity on the part of both priests and people (Ex 4:3, De 10:12, and similarly in NT). λειτουργέω "is the fulfilment of an office: it has a definite representative character, and corresponds with a function to be discharged". It is therefore used of serving in an office or ministry: in LXX always of priests and Levites, in NT, with its cognates (Ro 13:6 15:27, are not really exceptions), of services rendered either to God or man by apostles, prophets, teachers, and other officers of the church (cf. Tr., Syn., § xxxv; ICC on Ro 1:9; Westc., He., 232 ff.).

Abbott-Smith References

Liddell-Scott-Jones

λειτουργέω-έω,

earlier Attic dialect λητουργέω [Refs 4th c.BC+], etc. (λειτ- 22.665.11 (3rd c.BC)): perfect λελειτούργηκα [Refs 5th c.BC+]

__I at Athens, serve public offices at one's own cost, [λειτουργέωίας 4th c.BC: Demosthenes Orator 50.9, compare 5th c.BC: Lysias Orator 3.47 ">Refs 5th c.BC+]; λ. ὑπέρ τινος serve these offices for another, [Refs 4th c.BC+]; τὰ λελειτουργέωημένα public services performed, [Refs 4th c.BC+]
__II generally, perform public duties, serve the state, τῇ πόλει [λειτουργέωοῦν, ὃ καλοῦμεν εὐπόρους 4th c.BC: Aristoteles Philosophus “Politica” 1291a34; τοῖς σώμασιν καὶ τοῖς χρήμασιν λ. [prev. author] “Ath.” 29.5; λ. τοῖς σώμασιν 4th c.BC: Demosthenes Orator 21.165; τὸ περὶ τὰς ἀρχὰς λ. 4th c.BC: Aristoteles Philosophus “Politica” 1291a35 ">Refs 5th c.BC+]; λ. τῇ πόλει ταύτην τὴν λειτουργέωίαν[Refs 4th c.BC+]
__III generally, serve a master, with dative, οἱ ἑνὶ λειτουργέωοῦντες τὰ τοιαῦτα δοῦλοι [εἰσι] [Refs 4th c.BC+]; λ. τρισὶν ἀνδράσιν, of a prostitute, [Refs]
__III.2 perform religious service, minister, ἐπὶ τῶν ἱερῶν [λειτουργέωός.) ">NT+1st c.BC+]

_{LSJ Scripture Refs: Acts.13.2}