Just so you don't miss it, Mr. Lake has shared information about his current available tools. He has more as any wizard would, but both him and I see those doing either no good or more harm than help in this situation.
Investigation is not exactly the correct stat to use here, as Deception would be applicable to the situation. After all, she is thinking from a social perspective and trying to figure out how to best deceive her opponent(s).
Parum did not need to think long to figure out what could possibly work. First she and her friends would need to sneak upon their enemy in the cover of the smoke cloud they were causing by themselves and once the fight broke out, she could have "backup" shout out at them. Of course, no such thing would be coming, given how long the circling group did take on each rotation.
While she thought, Mr. Lake turned to face her instead of Brannor and nervously fidgeted with his fingers, rubbing each hand with the other in turns. Once inspiration rose to Parum's face, the wizard gave his answer: "Well, I could blind them with Colour Spray, but that's short lived... perhaps Crown of Madness... but that in turn has proven to not be very effective against those robed people, as if they were too devoted to care about my orders. Then last piece of control I can provide would probably be Sleep, but there's no guarantee if it'll affect all of them. Lastly, no self respecting Wizard leaves home without preparing Burning Hands. You should remember I can only muster two spells, one stronger than the other."
With that out of the way, Mr. Lake turned his focus back onto the temple, trying his best to time how long it took for the big group to make the rotation around the building. It was no short effort, but they couldn't exactly follow the situation much longer if they wanted to make it in before the front door was busted into pieces. Lake was fairly certain these people knew that too and found no need in rushing them. Better late than never, better prepared than dead. And dead people get nowhere.
3rd level Enchantment Wizard
Spells he has shared: 1st level - Colour Spray, Sleep, Burning hands 2nd level - Crown of Madness
@Dusksong It is pretty much like Lord of Evil guessed, a very small window akin to an arrow slit. Not quite as small, but even if the glass on it were to be broken one could not squeeze out of the hole. With what tools you have, enlarging the gap would be impossible.