“Many divergent things are said about the death of Theseus. Many say that he was bound in the underworld until Herakles restored him; but of the things I have heard, these are the most believable: Theseus attacked Thesprotia in order to kidnap the wife of the Thesprotian king and lost the majority of his army in the process. In fact, both he and Peirithous—who went on the expedition also looking for a marriage—were captured and the Thesprotian king kept them imprisoned in Kikhuros. There are many other things in the Thesprotian land worthy of seeing—the shrine of Zeus at Dodona and an oak sacred to the god. Near Kikhuros is a lake called Akherousia and a river called Akheron. A really unpleasant river called the Kokutos flows there too. Homer must have seen these places and was emboldened to use their names for places in Hades, transferring the names for the rivers from the Thesprotian landscape.
While Theseus was imprisoned, the children of Tyndareus attached Aphidna, sacked it, and installed Menestheus as king. Menestheus had no thought for the children of Theseus who had retreated to Elephenor in Euboia; but because he knew that Theseus, if he ever were restored from the Thesprotians, would be a difficult opponent, he attempted to improve the affairs of the common people, so that when Theseus was released, he was expelled from the land. As a result, Theseus went to Deukalion in Crete—when he was carried by winds to the island of Skyros, the Skyrians treated him well because of the fame of his family and the worth of the deeds which he accomplished himself. For these reasons, Lycomedes planned his death.”
ἐς δὲ τὴν τελευτὴν τὴν Θησέως πολλὰ ἤδη καὶ οὐχ ὁμολογοῦντα εἴρηται· δεδέσθαι τε γὰρ αὐτὸν λέγουσιν ἐς τόδε ἕως ὑφ’ ῾Ηρακλέους ἀναχθείη, πιθανώτατα δὲ ὧν ἤκουσα· Θησεὺς ἐς Θεσπρωτοὺς ἐμβαλών, τοῦ βασιλέως τῶν Θεσπρωτῶν γυναῖκα ἁρπάσων, τὸ πολὺ τῆς στρατιᾶς οὕτως ἀπόλλυσι, καὶ αὐτός τε καὶ Πειρίθους—Πειρίθους γὰρ καὶ τὸν γάμον σπεύδων ἐστράτευεν— ἥλωσαν, καὶ σφᾶς ὁ Θεσπρωτὸς δήσας εἶχεν ἐν Κιχύρῳ. γῆς δὲ τῆς Θεσπρωτίδος ἔστι μέν που καὶ ἄλλα θέας ἄξια, ἱερόν τε Διὸς ἐν Δωδώνῃ καὶ ἱερὰ τοῦ θεοῦ φηγός· πρὸς δὲ τῇ Κιχύρῳ λίμνη τέ ἐστιν ᾿Αχερουσία καλουμένη καὶ ποταμὸς ᾿Αχέρων, ῥεῖ δὲ καὶ Κωκυτὸς ὕδωρ ἀτερπέστατον. ῞Ομηρός τέ μοι δοκεῖ ταῦτα ἑωρακὼς ἔς τε τὴν ἄλλην ποίησιν ἀποτολμῆσαι τῶν ἐν ῞Αιδου καὶ δὴ καὶ τὰ ὀνόματα τοῖς ποταμοῖς ἀπὸ τῶν ἐν Θεσπρωτίδι θέσθαι. τότε δὲ ἐχομένου Θησέως στρατεύουσιν ἐς ῎Αφιδναν οἱ Τυνδάρεω παῖδες καὶ τήν τε ῎Αφιδναν αἱροῦσι καὶ Μενεσθέα ἐπὶ βασιλείᾳ κατήγαγον· Μενεσθεὺς δὲ τῶν μὲν παίδων τῶν Θησέως παρ’ ᾿Ελεφήνορα ὑπεξελθόντων ἐς Εὔβοιαν εἶχεν οὐδένα λόγον, Θησέα δέ, εἴ ποτε παρὰ Θεσπρωτῶν ἀνακομισθήσεται, δυσανταγώνιστον ἡγούμενος διὰ θεραπείας τὰ τοῦ δήμου καθίστατο, ὡς Θησέα ἀνασωθέντα ὕστερον ἀπωσθῆναι. στέλλεται δὴ Θησεὺς παρὰ Δευκαλίωνα ἐς Κρήτην, ἐξενεχθέντα δὲ αὐτὸν ὑπὸ πνευμάτων ἐς Σκῦρον τὴν νῆσον λαμπρῶς περιεῖπον οἱ Σκύριοι κατὰ γένους δόξαν καὶ ἀξίωμα ὧν ἦν αὐτὸς εἰργασμένος· καί οἱ θάνατον Λυκομήδης διὰ ταῦτα ἐβούλευσεν.
The details of Theseus’ death are reported elsewhere:
Plutarch, Life of Theseus 35.4
“When he came to [Lycomedes] he was seeking that his lands be returned to him so he might live there. Some report that Theseus was asking him for help against the Athenians. Lycomedes, either because he feared the man’s reputation or as a favor to Menestheus, led Theseus to the highest part of the land on the pretense of showing him the territory. Then he pushed him from the rocks and killed him. Others say that Theseus fell on his own, going on a walk after dinner.”
 πρὸς τοῦτον οὖν ἀφικόμενος ἐζήτει τοὺς ἀγροὺς ἀπολαβεῖν, ὡς αὐτόθι κατοικήσων: ἔνιοι δέ φασι παρακαλεῖν αὐτὸν βοηθεῖν ἐπὶ τοὺς Ἀθηναίους. ὁ δὲ Λυκομήδης, εἴτε δείσας τὴν δόξαν τοῦ ἀνδρός, εἴτε τῷ Μενεσθεῖ χαριζόμενος, ἐπὶ τὰ ἄκρα τῆς χώρας ἀναγαγὼν αὐτόν, ὡς ἐκεῖθεν ἐπιδείξων τοὺς ἀγρούς, ὦσε κατὰ τῶν πετρῶν καὶ διέφθειρεν. ἔνιοι δ᾽ ἀφ᾽ ἑαυτοῦ πεσεῖν φασι σφαλέντα, μετὰ δεῖπνον
Life’s Not All Minotaur-Slaying