In Genesis 18, does Jesus meet with Abraham? In Genesis 18, the Lord is mentioned several times. Along with 2 angels, he meets with Abraham. Is the Bible speaking of Jesus?
It does not explicitly state such, but it is possible to logically deduce it.

Jesus himself said that no one had ever seen the Father (John 6:46). In addition, Jesus said, "Before Avraham was, I am" (John 8:58). 

Technically, however, Avraham wouldn't have seen Yeshu'a of Nazareth, the incarnate Word of God. Rather, he would have seen the pre-incarnate Word. (Of course, I'd say most Christians don't find it necessary to make such a distinction.)

Many early Church fathers believed that Avraham and the other patriarchs saw God the Son when they are said to have seen God.

In Dialogue with Trypho, Ch. LVI §1, Justin Martyr wrote,


  Therefore, Moshe, the blessed and faithful servant of God, declares that he who appeared to Avraham by the oak in Mamre simultaneously with the two angels in his company, is God, having been sent for the judgment upon Sedom by Another who eternally dwells in the supercelestial places, and never appears, holding personal intercourse with none, whom we believe is the Maker and Father of all things.


Roberts-Donaldson English Translation


  Μωυσῆς οὖν, ὁ μακάριος καὶ πιστὸς θεράπων θεοῦ, μηνύων ὅτι ὁ ὀφθεὶς τῷ Ἀβραὰμ πρὸς τῇ δρυῒ τῇ Μαμβρῆ θεὸς σὺν τοῖς ἅμα αὐτῷ ἐπὶ τὴν Σοδόμων κρίσιν πεμφθεῖσι δύο ἀγγέλοις ὑπὸ ἄλλου, τοῦ ἐν τοῖς ὑπερουρανίοις ἀεὶ μένοντος καὶ οὐδενὶ ὀφθέντος ἢ ὁμιλήσαντος δι' ἑαυτοῦ ποτε, ὃν ποιητὴν τῶν ὅλων καὶ πατέρα νοοῦμεν.


Greek Text

Two persons, both God, one who is sent (the Son), and the other who sends (the Father).