No Harry isn't dumb, but he is a stubborn idiot especially when he's already made up his mind.
Lash also isn't stupid enough to waste time using illusions to stop Harry when she already knows that it won't work and Harry will do it anyway.
Lash has the ability to completely stop Harry from doing anything see Turn Coat where Nico fully expected Lash to be able to completely neuter Harry.
Making Harry think he's fighting illusions and winning while using his body to fix LC is no harder then making Harry fight illusions.
Lash even told Harry he was going to die and the model was going to blow up and Harry didn't care he was going to do it anyway.
Even even threatened to do it while she was mucking around with his concentration.

Lash was able to accelerate Harry's brain, block mental attacks and has advanced magical knowledge that goes back to the begining of time.
Lash even knows the how and why Harry can hurt Outsiders with magic.
Lash actively keeps Harry from finding out what she can and can not do, because every time Harry learns these things its one less effective tool in her tool box.

Harry fixed Little Chicago or more accurately Lash used Harry to fix it.

Lash is the only one with the means, know how and chance to fix it.
It wouldn't be the first time Lash had intervened to protect Harry from death.
Basically Lash knew it was broken, she tried to get Harry to take up the coin to protect himself and when he refused she chose to fix it to prevent Harry from dying.