I think that storyline just kinda ends there for now. I think Big Cock Cthulu is kind of implied to be the big bad of the game, so we'll probably get more when the game gets closer to being finished.
i mean the mind protection story, after you complete it the rest of lizards story is unlocked. so yeah you should do it! sorry about my wording, if there is something in this game that isn't out yet you should always do it unless its a one time thing and you need it later, like an important plot thing. there isn't any of those but like if there ever is that's the only thing you should avoid!