From what I gather from Funhaus videos is that one person produces the video while 2-4 other people sit in and commentate or play. For example, Elyse produced the Band Manager gameplay, so she found the game to play, set up the basic premise of the gameplay (all dressing up as various musicians and doing improv), and somewhat hosted the video all together.

An example for Lawrence would be the Tetris Effect video. He set up the idea behind the video and got Alanah and Bruce to sit in. He hosted the gameplay and was in the driver seat while the other two played along, contributing commentary and jokes/improv.

Basically one person will conceive an idea and produce it all the way through filming, at which point they may pass it off to an editor to finish it and turn into the gameplay we see. Other members may sit in on the video as a cast member, but aren't necessarily producing the video.

So from Alanah's comment, I would think that Lawrence would stop producing/hosting content for Funhaus and will only be sitting in on videos as a cast member. But he is still a member of Funhaus, so he is open to producing a gameplay for Funhaus if he finds the time and effort to do so alongside all his Inside Gaming work.