I really would not like a timer it would make the game too clinical for me. Maybe a message warning that the monster lair is threatening the local population and will likely grow larger in the near future if not dealt with.

Also it would be nice to have an option in the game to set the pace of the monster upgrade

I would be fine simply with a change in Lair graphics which indicated that the area had levelled up. That way if you were paying attention you would know hat they were stronger, but would not really have forewarning. (City gatherers have noticed that there are more bears up in the hills than usual). I would not mind a popup to that effect, but do not see it as vital.

Added effect of the monsters levelling up mechanic, it accurately represents the population of creatures being pushed back by settlements into smaller and smaller habitats forcing them to overpopulate an area, and thus have to "come down out of the hills" looking for food.