Twice in the bible, God makes reference to "seventy times seven" (or "seventy-seven times"). Once in Genesis 4:24 (dealing with Cain's punishment for his murder of Abel), and the other in Matthew 18:22 (in an answer to Peter's question of how many times he should forgive a brother or sister that sins against him). Is there any significance to this phrase, and if so, what?
In many ancient cultures, Hebrew included, the number seven often signifies completeness and/or perfection (for more information see either Numerical Sayings in the OT, W. Roth or IVP New Bible Dictionary, ed. Marshall, Miller, Packer, Wiseman, p834). Therefore, it is often used in an emphatic sense. This is seen in Peter's question: "should I forgive seven times?" (possibly thinking he was being a good disciple in making the point that he should always forgive) - Jesus' reply is to be emphatically emphatic! That is, seventy times seven! Jesus often uses hyperbole (overstatement to make a point) in his teaching style, such as the Camel and the eye of a needle in Matthew 19:24.
Lamech's use, again, is to show he is being emphatic. His use of seventy-seven is to make a point.
Hope this helps.
It's also interesting to note that Jesus' contemporary rabbis would teach that a man should forgive a sin 3 times. (See Carson's commentary on Matthew, p.405). This makes Peter's statement of "forgiving an infinite amount of times" even more impressive, though Jesus is not outdone, of course!
Your two examples are two different numbers. Lamech speaks of seventy-seven times (77), while Jesus says seventy times seven (490). It's hard to say exactly what Lamech meant, as his story is badly incomplete--it doesn't say who he killed or why, or what happened after that. So it's difficult to draw any conclusions here.
As for Jesus's answer to Peter, let's read it in context.
21Then came Peter to him, and said, Lord, how oft shall my brother sin against me, and I forgive him? till seven times?
22Jesus saith unto him, I say not unto thee, Until seven times: but, Until seventy times seven.
I don't think the exact number matters as much as the principle. Peter asked, should I forgive my brother some fixed, easily-countable number of times? And Jesus said no, forgive him an arbitrarily large number of times, too high to easily keep track of.
Tyndale has seventy times seven, and this is, I believe, inspired by God. The reason that both scriptures mention seventy times seven is that both are referring to the same event typologically.
Cain represents Israel, who killed his brother Abel (Jesus the Messiah) and was then cast out to wander the earth. Yet God puts His seal of protection on both Cain and Israel; anyone who harms them will be avenged seven-fold by God, see also Ps 79.
Lamech, the sixth from Cain, also represents Israel; but this is the present humanistic, boastful, arrogant Israel who works out his own vengeance and thinks himself therefore greater than God.
This represents the present State which exists by its own might and is preparing a vengeance on the world for the events of the last two thousand years. The 490 is a prophetic period of time representing the period of God's grace and forgiveness available to both Jew and Gentile...this period will run out soon, around the year 2030. It is derived from a 'generation' of 'jubilees' i.e. 40 x 49 = 1960 years from when 'Cain' and Israel were exiled to wander.
Simply factor 1960 differently and you will find 4 x 7 x 70 = 4 x 490 (see Leviticus 26 and Judah's first exile of 70 years). He who has ears, let him hear what the Spirit says to the churches.