For the Reynolds siblings, there are plenty of factors at play here. On the pro-death side of things, they stand to get some sort of inheritance if Pop-Pop dies. It also helps(?) that the guy was a Nazi, not just during the war but long after, even bringing Dennis and Dee to a Hitler Youth camp when they were children. This is a big point in the pro-euthanasia direction, as the siblings would prefer to kill off any memory of their shameful past.
But on the other hand, they don’t love the idea of actively murdering someone, even if it’s technically a good cause. They seriously consider euthanizing a dog at a local animal shelter first (to see how they feel about it), but can’t quite go through with it. In a classic “Always Sunny” joke, it’s later revealed that the dogs they let loose from the pound went on to bite a bunch of people and get put down anyway. Dennis and Dee’s self-serving idea of kindness didn’t actually help anyone.
Luckily, the perpetually-annoyed lawyer (just known throughout the show as The Lawyer, played by Brian Unger) is there to make the Reynolds’ decision for them. Dennis and Dee try to act like their hands are entirely clean, until the doctor compliments The Lawyer’s decision to pull the plug, and then the siblings immediately switch their tune and try to claim credit. It’s shamelessly self-serving and shallow behavior, and perfectly in line with the characters throughout the rest of the show.