Lairs · Board game rules
Do you have to fight the Monster in a known Lair space?
Quick answer
No—if a Monster is in a Known space, you don't have to fight it immediately, but you can only fight it or leave its space; no other actions are allowed.
Details
When you move into a space containing a Monster (or Trap) that was already Known, it does not immediately strike you, but while you remain there, the only things you're allowed to do are either fight/disarm it, or take an action that moves you out of its space [p.9 — Hazards]. So fighting is not literally forced—you could instead Backtrack, Creep, Hustle, etc. out of the space if that's possible—but you cannot take any other kind of action while occupying it.
This differs from moving into an Unknown space with a Monster, which strikes you immediately upon entry, and then you still face the same choice: fight it or leave [p.9 — Hazards].
Watch out: A Monster or Trap doesn't block you from leaving its space unless its card specifically says so, so normally you always have the option to flee instead of fighting, as long as you have a legal move available [p.9 — Hazards].