Lyle: Admittedly, modernizing the language of premodern plays lessens their aesthetic quality, but such modernizing remains valuable for teaching history, since it makes the plays accessible to students who would otherwise never enjoy them.
Evaluate
Most of the time, the two people disagree over an explicit claim. Sometimes, there's nothing explicit and we have to ask ourselves about assumptions. But we can start by taking each of Person 1's claims and asking ourselves if Person 2 tried to go against that idea.
Did Carl try to argue that modernizing the language of premodern plays does not lessen their aesthetic quality?
No, Carl never talks about aesthetic qualities (what makes them beautiful or artistically worthwhile)
Did Carl try to argue that modernizing the language of premodern plays is not valuable for teaching history?
Yes, he explicitly says that .
Did Carl try to argue that modernizing plays does not make them accessible to students who would otherwise never enjoy them? (i.e. is he saying that modernizing doesn't make someone who wasn't likely to see it now be likely to see it?)
No, Carl doesn't comment at all on whether the potential audience for a premodern play widens / doesn't widen, as a result of modernizing its language.
Goal
Since Carl only disagreed with Lyle's 2nd claim, we'll focus our prephrase on that language:
whether or not modernizing remains valuable for teaching history (because it widens the audience) or whether it is of no value for teaching history (because students can't gain deep knowledge of the past if the play has been modernized).