Yes, outside the NT is the only place you can go for help with εξεκαυθησαν. I found about 70 samples of πυροω εκκαιω in the LXX. It has nothing to do with sexuality. Most frequently used as metaphor of divine anger. In other contexts the fire is a result of divine anger. In some contexts it depicts this burning as a purifying process.
NOTE, the NRSV is not a translation of the LXX. I don’t have NETS handy for copying.
Num. 11:1 Καὶ ἦν ὁ λαὸς γογγύζων πονηρὰ ἔναντι κυρίου, καὶ ἤκουσεν κύριος καὶ ἐθυμώθη ὀργῇ, καὶ ἐξεκαύθη ἐν αὐτοῖς πῦρ παρὰ κυρίου καὶ κατέφαγεν μέρος τι τῆς παρεμβολῆς.
Num. 11:1 (NRSV) Now when the people complained in the hearing of the LORD about their misfortunes, the LORD heard it and his anger was kindled. Then the fire of the LORD burned against them, and consumed some outlying parts of the camp.
Num. 11:3 καὶ ἐκλήθη τὸ ὄνομα τοῦ τόπου ἐκείνου Ἐμπυρισμός, ὅτι ἐξεκαύθη ἐν αὐτοῖς πῦρ παρὰ κυρίου.
Num. 11:3 (NRSV) So that place was called Taberah, because the fire of the LORD burned against them.
Deut. 29:19 οὐ μὴ θελήσῃ ὁ θεὸς εὐιλατεῦσαι αὐτῷ, ἀλλ᾿ ἢ τότε ἐκκαυθήσεται ὀργὴ κυρίου καὶ ὁ ζῆλος αὐτοῦ ἐν τῷ ἀνθρώπῳ ἐκείνῳ,
Deut. 29:20 (NRSV) the LORD will be unwilling to pardon them, for the LORD’S anger and passion will smoke against them.
2Sam. 24:1 Καὶ προσέθετο ὀργὴ κυρίου ἐκκαῆναι ἐν Ισραηλ, καὶ ἐπέσεισεν τὸν Δαυιδ ἐν αὐτοῖς λέγων Βάδιζε ἀρίθμησον τὸν Ισραηλ καὶ τὸν Ιουδα.
2Sam. 24:1 (NRSV) Again the anger of the LORD was kindled against Israel, and he incited David against them, saying, “Go, count the people of Israel and Judah.”
Is. 1:25 καὶ ἐπάξω τὴν χεῖρά μου ἐπὶ σὲ καὶ πυρώσω σε εἰς καθαρόν, τοὺς δὲ ἀπειθοῦντας ἀπολέσω καὶ ἀφελῶ πάντας ἀνόμους ἀπὸ σοῦ καὶ πάντας ὑπερηφάνους ταπεινώσω.
Is. 1:25 (NRSV) I will turn my hand against you;
I will smelt away your dross as with lye
and remove all your alloy.
Ezek. 21:3 καὶ ἐρεῖς τῷ δρυμῷ Ναγεβ Ἄκουε λόγον κυρίου Τάδε λέγει κύριος κύριος Ἰδοὺ ἐγὼ ἀνάπτω ἐν σοὶ πῦρ, καὶ καταφάγεται ἐν σοὶ πᾶν ξύλον χλωρὸν καὶ πᾶν ξύλον ξηρόν, οὐ σβεσθήσεται ἡ φλὸξ ἡ ἐξαφθεῖσα, καὶ κατακαυθήσεται ἐν αὐτῇ πᾶν πρόσωπον ἀπὸ ἀπηλιώτου ἕως βορρᾶ· 4 καὶ ἐπιγνώσονται πᾶσα σὰρξ ὅτι ἐγὼ κύριος ἐξέκαυσα αὐτό, καὶ οὐ σβεσθήσεται. 5 καὶ εἶπα Μηδαμῶς, κύριε κύριε· αὐτοὶ λέγουσιν πρός με Οὐχὶ παραβολή ἐστιν λεγομένη αὕτη;
Ezek. 20:47 (NRSV) say to the forest of the Negeb, Hear the word of the LORD: Thus says the Lord GOD, I will kindle a fire in you, and it shall devour every green tree in you and every dry tree; the blazing flame shall not be quenched, and all faces from south to north shall be scorched by it. 48 All flesh shall see that I the LORD have kindled it; it shall not be quenched.
Jer. 51:6 καὶ ἔσταξεν ἡ ὀργή μου καὶ ὁ θυμός μου καὶ ἐξεκαύθη ἐν πόλεσιν Ιουδα καὶ ἔξωθεν Ιερουσαλημ, καὶ ἐγενήθησαν εἰς ἐρήμωσιν καὶ εἰς ἄβατον ὡς ἡ ἡμέρα αὕτη.
Jer. 44:6 (NRSV) So my wrath and my anger were poured out and kindled in the towns of Judah and in the streets of Jerusalem; and they became a waste and a desolation, as they still are today.
Zech. 13:9 καὶ διάξω τὸ τρίτον διὰ πυρὸς καὶ πυρώσω αὐτούς, ὡς πυροῦται τὸ ἀργύριον, καὶ δοκιμῶ αὐτούς, ὡς δοκιμάζεται τὸ χρυσίον· αὐτὸς ἐπικαλέσεται τὸ ὄνομά μου, κἀγὼ ἐπακούσομαι αὐτῷ καὶ ἐρῶ Λαός μου οὗτός ἐστιν, καὶ αὐτὸς ἐρεῖ Κύριος ὁ θεός μου
Zech. 13:9 (NRSV) And I will put this third into the fire,
refine them as one refines silver,
and test them as gold is tested.
They will call on my name,
and I will answer them.
I will say, “They are my people”;
and they will say, “The LORD is our God.”
Is. 1:25 καὶ ἐπάξω τὴν χεῖρά μου ἐπὶ σὲ καὶ πυρώσω σε εἰς καθαρόν, τοὺς δὲ ἀπειθοῦντας ἀπολέσω καὶ ἀφελῶ πάντας ἀνόμους ἀπὸ σοῦ καὶ πάντας ὑπερηφάνους ταπεινώσω.
Is. 1:25 (NRSV) I will turn my hand against you;
I will smelt away your dross as with lye
and remove all your alloy.