Lexical Definition

‎λυσιτελεῖ‎ lysiteleî (loo-sit-el-i') to profit ^G:V
third person singular present indicative active of a derivative of a compound of ‎λύσις‎ and ‎τέλος‎

it is better.

• impersonally, it answers the purpose, i.e. is advantageous

Abbott-Smith

** λυσιτελέω, -ῶ (< λυσιτελής, useful, prop., τὰ τέλη λύων), [in LXX: To 3:6, Si 20:10, 14 29:11*;]
1. prop., to indemnify, pay expenses.
2. to be useful, to profit; usually impers., λυσιτελεῖ, it profits: c, dat. pers., seq. εἰ . . . ἤ, Lk 17:2.†

Abbott-Smith References

Liddell-Scott-Jones

λυσιτελεῖ-έω,

properly indemnify for expenses incurred, or pay what is due, and then 'pay', i.e. profit, avail (compare λύω see 2), with dative,

__I with subject expressed, οὔ φημ᾽ ἂν λυσιτελεῖν σφῷν [τοῦτο] [Refs 5th c.BC+]
__I.2 mostly impersonal, λυσιτελεῖ μοι it profits me, is better for me, with participle, οἷς οὐδ᾽ ἅπαξ ἐλυσιτέλησε πειθομένοις [Refs 5th c.BC+]: with infinitive, λ. προϊέναι [Refs]; τεθνάναι νομίσασα λυσιτελεῖν ἢ ζῆν thinking it better to be dead than alive, [Refs 5th c.BC+], etc.: with dative person, it profits one to do so and so, οὐ γάρ οἱ λυσιτελέειν.. δικάζειν [Refs 5th c.BC+]: sometimes with accusative person, it is good that.., λυσιτελεῖ τὸν μέλλοντα κακῶς ἰητρεύεσθαι ἀμφότερα καταγῆναι τὰ σκέλεα [Refs 5th c.BC+]
__I.3 in bad sense, conspire, as gloss on{ἐς τὸ κακὸν ἀλλήλοισι συντιμωρεῖ} [Refs 5th c.BC+]
__II neuter participle as substantive, τὸ λυσιτελοῦν profit, gain, advantage, [Refs 5th c.BC+]; a wrong etymology is given in [Refs 5th c.BC+]