Of course every time Jesus performed an out-of-this-world miracle—like calming the stormy sea or speaking the dead to life—such miracles hinted at his deity. Similarly every time Jesus was 
named the Son of God, or when He declared Himself to be the Son of the Father, these hinted at His deity (The Jews understood this to be more than a hint; see e.g. John 5:18; 10:33.).
In Sunday’s gospel when Jesus healed the ten lepers, one returned “praising God with a loud voice. He fell facedown at Jesus’ feet in thanksgiving to Him.” This in itself seems to indicate Jesus is God, as the healed leper praises God by giving thanks to Jesus. Jesus then confirms this understanding as He asks, “Was no one found except this foreigner to return and give glory to God?” The Samaritan, cured of his leprosy, returned to Jesus and at His feet he gave glory to God—to Jesus. Another apparent hint at the deity of Jesus occurs in the command of Jesus that the lepers go to the temple—God’s unique dwelling place on earth. But as this former-leper returns to Jesus, Jesus is not critical of his failure to go to the Temple, for the man is indeed going to the Temple, the place where God dwells among men—in the person of Jesus Christ. The following are a few other hints of the deity of Jesus peppered throughout the Gospel of Luke.
When Saint Luke explains the identity of John the Baptist in Luke 3, the evangelist is inspired to point to him as the fulfillment of Isaiah’s prophecy that describes the way-preparer as “A voice of one calling in the wilderness, ‘Prepare the way of the Lord…’” Though “Lord” as a title for Jesus may not always be speaking of His deity, it must here be speaking of His deity, because in Isaiah’s prediction the Hebrew word for Lord is the unique name for God—Yahweh. John the Baptist was preparing the way of Yahweh, the way of Jesus; Jesus is God (Yahweh).
In Luke 7:16, after Jesus had raised to life the dead youth from the town of Nain, the people exclaim, “God has visited His people.” One might understand this to mean that God, through a great prophet, has visited His people. But one can also take it as a confession by the people that Jesus is God, because God as a man was literally visiting His people—for who except God can speak the dead to life?
We find the record in Luke 8:26ff of another merciful, miraculous deliverance as Jesus cast the legion of demons out of the cemetery-residing man of the Gerasenes. The man then begs to go with Jesus, but the Lord responds to him, “Return home and tell how much God has done for you.” What does the exorcised man do? “So the man went away and proclaimed all over the town how much Jesus had done for him.” These are in back-to-back sentences in which the parallel is obvious: “…tell how much GOD has done for you…[he] proclaimed how much JESUS had done for him.” Hint: Jesus is God.
In Luke 18:18ff the rich young ruler petitions Jesus, “Good Teacher, what must I do to inherit eternal life?” Jesus replies, “Why do you call me good? No one is good except God alone.” There is here a hint that if Jesus is the Good Teacher, and because only God is good, then Jesus must be God.
Thanks be to God that in Jesus the fullness of deity dwells bodily, for only God’s death could redeem mankind out of sin, death and the devil’s domain. Truly, as proleptically prophesied by Zechariah, “…the God of Israel….has visited and redeemed His people.” (Luke 1:68)