I'd argue you can add procedural generation to the starting distribution of living cells. You could also vary the rules for living vs dead cells by a variable that changes depending on the 'level' you're at, or just randomize it's value each game. You could also add walls to the level that act like the boundary, and the layout of the walls would be procedurally generated. It would affect what patterns get created in potentially interesting ways but you'd need large rooms or spaces so that everything doesn't die off too soon.
For gameplay, I'd suggest the typical rogue goal of 'reach level X then leave'. So, the board could change in size or shape or number of living cells at the start based on depth, and the goal is to reach a certain depth. To change depth, have a cell that you need to reach which is the stairs down (and it's like a wall: it doesn't get created or destroyed, it just waits for the player to reach it). The player could attack other cells to kill them off, so that they can make their way safely to the stairs, but make sure that there is a rule regarding re-spawning living cells so that the player can't just clear the board and then leave. I'd also argue against the goal being to kill everything, since it might be trivial or impossible depending on the pattern created; having to avoid those enemies while