I've always heard that Lorne is famously against improvisation while shooting. There have been numerous examples over the years of people getting in trouble for doing it. Here's one article [1]. There are very minor changes that don't seem to cause problems. Bill Hader talked about Fred Armisen's delivery of "What are you doing here?" in the first Californians sketch being different when shooting causing him to have trouble keeping from laughing.

This article [2] says, “Oh, ’cause we Black?” was added ahead of the run-through, but camera direction changed and not everyone was informed who the camera would be showing as it was delivered.

[1] https://www.slashfilm.com/1225418/why-lorne-michaels-doesnt-...

[2] https://www.vanityfair.com/hollywood/2023/02/snl-lisa-from-t...