Let's look at the Greek here:
The original word for "this generation" is genea. Strong's concordance for this shows:
1) fathered, birth, nativity
2) that which has been begotten, men of the same stock, a family
a) the several ranks of natural descent, the successive members of a
b) metaph. a group of men very like each other in endowments, pursuits,
1) esp. in a bad sense, a perverse nation
3) the whole multitude of men living at the same time
4) an age (i.e. the time ordinarily occupied be each successive generation), a
space of 30 - 33 years
Definitions 3 and 4 here obviously would include only the people alive at the time that the words were spoken. Definitions 1 and 2 could include people that were not currently alive.
If we look at other places where this word is translated, we can see that it's also translated as "times".
Acts 14:16 (NIV) In the past times, he let all nations go their own way.
Acts 15:21 (NIV) For the law of Moses has been preached in every city from the earliest times and is read in the synagogues on every Sabbath.
We can also see genea being translated as "nation" in the old King James Version:
Phillipians 2:15 (KJV)
That ye may be blameless and harmless, the sons of God, without rebuke, in the midst of a crooked and perverse nation, among whom ye shine as lights in the world;
However, the original KJV is the only version that uses this this translation (as even the New King James Version uses "generation").
"Generation" is the best translation, although "times" could be used. According to the definition, "lineage" could also be a translation. However, given that genea is not translated as "lineage" in any major translation, I would hesitate using that.