We can’t be sure, but it is unlikely that Luke saw Jesus personally. There’s no information in the Bible to suggest that he did.
However, every Christian claims to know Jesus personally, to some degree (in fact, knowing God and Jesus is a vital part of a Christian’s life: John 17:3). Obviously, when Jesus returns to the earth to set up God’s kingdom,1 believers will start a new period in their lives where they will grow to know Jesus even more (1John 3:2). But, while Jesus is away, believers can still know him: God teaches us about his son through the scriptures (e.g. John 20:31), and believers can experience God and Jesus working in their lives to help them grow and mature in their discipleship (Mat. 28:18; Eph. 2:10; Phil. 1:6; Heb. 12:5-11). In this way, like every Christian, Luke knew Jesus.
1. For more info, see ‘Where will the Kingdom of God be — in heaven or on earth?‘.