So, first, "lively discussion" shouldn't be sticking around for years. Comments are intended to be temporary notices for improving the post and then removed after their usefulness is done. So, generally, this whole problem case doesn't occur if cleanup is happening regularly.
The age of the answer/comments is not going to be a good predictor of how likely that comment is to be useful.
Even assuming the comments that the person are responding to are useful and purposefully left, responses to it can still be useful no matter how old the post or the previous comments are. I've seen comments on 6-7 year-old answers prompt edits, improvements to posts and spur other questions even. Sometimes comments on a post are useful to people other than the poster of the question/answer. Regardless, the age of the previous comments does not say anything about the likelihood of that comment to be useful. Sometimes even long-inactive OPs come back and respond or make edits in response to a comment.
Warning a person about the age of the comments is guaranteed to dissuade some percentage of commenters from leaving that comment and with no guarantee that the age has any relevance to how their comment will be received/acted on. So I think this suggestion would not really bring any benefit.