λῡσῐτελ-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] [[ 5th-6th c.BC: Aristophanes Comicus “Plutus” 509; λυσιτελεῖ ἡμῖν ἡ δικαιοσύνη 5th-6th c.BC: Plato Philosophus “Protagoras” 327b; δοῦλος τοιοῦτος οἷος μηδενὶ δεσπότῃ λυσιτελεῖν 5th-6th c.BC: Xenophon Historicus “Memorabilia” 2.1.15. ] Refs 5th c.BC+]
__I.2 mostly impersonal, λυσιτελεῖ μοι it profits me, is better for me, with participle, οἷς οὐδ᾽ ἅπαξ ἐλυσιτέλησε πειθομένοις [[ 5th c.BC: Lysias Orator 25.27; πολλοῖς δὴ ἐλυσιτέλησεν ἀδικήσασι 5th-6th c.BC: Plato Philosophus Alcaeus1.113d ] Refs 5th c.BC+]: with infinitive, λ. προϊέναι [[ [prev. author] “Tht.” 181b ] Refs]; τεθνάναι νομίσασα λυσιτελεῖν ἢ ζῆν thinking it better to be dead than alive, [[ 5th-6th c.BC: Andocides Orator 1.125, compare 5th-6th c.BC: Plato Philosophus “Respublica” 407a, 5th-6th c.BC: Xenophon Historicus “Institutio Cyri (Cyropaedia)” 2.4.12 (variant), “PHamb.” 27.17 (3rd c.BC)] Refs 5th c.BC+], etc.: with dative person, it profits one to do so and so, οὐ γάρ οἱ λυσιτελέειν.. δικάζειν [[ 5th c.BC: Herodotus Historicus 1.97; ὅτι μοι λυσιτελοῖ ὥσπερ ἔχω ἔχειν 5th-6th c.BC: Plato Philosophus “Apologia” 22e, compare 5th-6th c.BC: Xenophon Historicus “Hiero” 7.13 ] Refs 5th c.BC+]: sometimes with accusative person, it is good that.., λυσιτελεῖ τὸν μέλλοντα κακῶς ἰητρεύεσθαι ἀμφότερα καταγῆναι τὰ σκέλεα [[ 5th c.BC: Hippocrates Medicus “περὶ ἀγμῶν” 19, compare 5th-6th c.BC: Plato Philosophus “Respublica” 406d: _absolutely_, ἐλυσιτέλει γάρ 4th c.BC: Axionicus Comicus 6.6. ] Refs 5th c.BC+]