by thefred138
I don't have the rules (or Quest Guide, for that matter) on hand, but we just completed this Chapter over the weekend.I believe that in the Chapter 2 special set-up instructions,it specifies that a surge happens on the tile where your party is located. I think the key is to remember that Lily isn't considered part of the party since she is captured.
Per those those instructions (again, I'm going off of memory here) if the surge consists of small minions, you place all but one of the minions as normal and then add a cockroach to Lily's tile for her to deal with. If the surge is a large minion, that minion gets placed as normal and an additional cockroach is added to Lily's tile. So, if a surge occurred that called for 4 rat warriors, you would place 3 warriors on the tile where your party is currently located and a single cockroach on Lily's tile. Otherwise, you won't place any minions on that tile until your party enters the square, and a large minion cannot be added for Lily to deal with on her own. As we found out over the weekend, it is definitely possible for more than one roach to be on her tile and going after just her, however!
As I said before, I think the confusion might be because it sounds like you were considering Lily to be a party member, which is a mistake we made the first time we played as well. I believe (again, without the rules in front of me) that your "party" is necessarily always on the same tile, since any explore action taken by a mouse moves the entire party to the new tile.
As for the third mouse trap, we had the same issue come up and dealt with it as you did. We both thought it was a little odd that there wasn't an extra included in the box.
Then again, I could be mistaken as well.