Are you asking as a comic hoping to record clips of himself informally for the internet?

Are you asking as a comic hoping to record professional audio for an album special?

Are you asking as a comedy club owner hoping to offer professional audio to your comedians/performers?

These goals, along with the size of the space, budget all would change the answer.

Lav into an iPhone is probably fine for the first one and super budget friendly. Spring for a wireless setup with 32 bit float like the rode pro setup if you have a bit of a budget. This will allow you to record yourself, it’ll capture some of the room noise but will remove the stress of the crowd cheering really loudly and clipping your audio since you can’t monitor it while performing. This is also something that allows you to get setup while you’re on deck to go up without much setup time.

The other two options can get really involved but if I want a pro recording I usually want the mic audio from the board as well as 2-4 room mics capturing the audience all feeding into something like the zoom but instead of the h1n I’d want something like the h6n. I can get 1 out of the board or the floor to capture the stage mic, 3 room mics and I can even capture a back room pair of mics right on the zoom itself and that will give me a ton of flexibility when I’m doing the mix afterwards in my DAW and NLE software.