The background of Luke 11:50 was at the moment Jesus criticized the Pharisees of their wrong doing (Luke 11:37-44), one law teacher rebuked Jesus that he did not agree with his accusation. Then Jesus replied them (Luke 11:47-48 NIV)
47 “Woe to you, because you build tombs for the prophets, and it was your ancestors who killed them.
48 So you testify that you approve of what your ancestors did; they killed the prophets, and you build their tombs.
What did Jesus mean in this context? Perhaps the parallel verses from Matthew 23:27-31 can shed more light of it.
27 “Woe to you, teachers of the law and Pharisees, you hypocrites! You are like whitewashed tombs, which look beautiful on the outside but on the inside are full of the bones of the dead and everything unclean.
28 In the same way, on the outside you appear to people as righteous but on the inside you are full of hypocrisy and wickedness.
29 “Woe to you, teachers of the law and Pharisees, you hypocrites! You build tombs for the prophets and decorate the graves of the righteous.
30 And you say, ‘If we had lived in the days of our ancestors, we would not have taken part with them in shedding the blood of the prophets.’
31 So you testify against yourselves that you are the descendants of those who murdered the prophets.
Who built the tombs? Answer: the Pharisees.
What Jesus meant was, the Pharisees built elaborate tombs of the prophets as the acknowledgement the prophets were indeed from God. Their motive was neither honor the prophets nor confess the sin of their ancestors did. They were hypocrites. They did it just for their own honor, appeared to people they were righteous. Deep inside, they approved what their ancestors did.
Within these context, surely the word "generation" refer to the Pharisees and the teachers of the law at that time. However, these words from Jesus had an implication to all the generations thereafter.
Sin from the past, though it werewas not done by this generation, but if we approved it in mind, we committed the same sin.