This passage is found in the Revised Common Lectionary year C during Lent (Most recently: Feb 28, 2016)
Summary: This passage must be read in conjunction with 13:10-13, where Jesus heals someone who has been sick for some time. The point is that Jesus does not give up on us, but always calls us to repent. To put it another way -- repentance is not grounded in fear, but in hope. Hope that judgment may be avoided; hope that the future will not simply be a repetition of the past; hope that God has power greater than sin.
(I also think there is a sermon on the word "found" as well, see below)
A few things worth noting here:
πεπονθασιω (perfect form of πασχω, meaning "to suffer"; 13:2) The word here for suffer is "pasch-oo" (hence the English 'passion'). Interestingly this is the only time in the Gospel of Luke where someone else besides Jesus is suffering. Also interesting is that the verb is in the perfect, meaning they suffered, but are still in the state of suffering. Trying to unpack that one.
μετανοητε ("repent"; 13:3,5) The form of this verb is important. The Greek for "repent" here is a present tense subjunctive, not an aorist imperative. Literally: "If you are not continually repenting..." In short, Jesus is not calling them to repentance once (or over one sin) but calling them to a lifetime of repentance (the thesis #1 of Luther's 95 theses...)
απολλυμι ("destroy"; 13:3/5) The word here for destroy is "apollu-mi." This word means destory or lose. (Lose is in the middle voice) In chapter 9, Jesus warns his disciples that they must "lose" their life (same verb)
ευρισκω ("find"; 13:6) The word find (ευρισκω) is very common in the Gospel of Luke (almost as much as M, M and J combined). Luke presents Jesus as a God who finds us, finds us suffering, lost and in need of repentance. But he brings us in any way!
αφες (αφιημι; 13:8) The servant here, as he is telling the master to "leave it alone," is also in the Greek saying, "forgive it." Forgiveness means "give it another chance!"