Meaning in life with finite or infinite life. I think an immortal life would be meaningless, if we assume the person's memory is immortal.
What is the meaning of your life? Well, that depends on how you can describe it. A person who lied on the couch watching TV their whole life; their life would be summed up as so. There is not a lot of aesthetically pleasing content to unpack from that description, nor is there a lot of (good) impact, and thus, their life could be described as rather meaningless. A person who spent much of their time working on a cure for cancer however, would have a life whose description could be unpacked for ages. All of the lives prolonged, all of the lives created, all of the events and emotions permitted to come about, all because of the life-saving medicine they created. There is so much to unpack from this life; thus, it is meaningful.
If you life forever however, something strange happens. Look at the full breadth of your possible actions; there are diametrically opposed actions you could commit, but one (or both) of them are extremely unlikely. Across eternity however, the probability that you'll commit any one possible action goes to 1. So, in your infinite life, you'll be everything from a savior to a genocidal dictator, and at the limit at infinity, I suspect the interference of all your actions would be completely destructive. That is, the valence of your impact would be 0.
So, could your immortal life be meaningful when you'd know that all that you do will be undone by yourself? Well, maybe the breadth of all your possible actions isn't as big as I believe; maybe it is biased towards good, meaning your impact will be positive. Or, perhaps what you will do and have done is irrelevant; perhaps meaning only lies in the present?
It's a difficult topic, but I think my suspicion could be summed up like this:
A finite life has finite meaning, and thus a meaning. An infinite life has infinite meaning, and thus no meaning? To be everything is to be nothing? What is the meaning in to be or not to be when you will always choose both?