I will confirm that it appears to be a sound issue. Even with audio on Low Fidelity, there is simply too much happening. So, in order to help resolve the issue I turned off Music and Voice. This helped, but the Sound Effects are the what is causing this lag. My device is a Creative Sound Blaster Audigy 2 ZS with 2008 Drivers (up-to-date).
I tested this by hovering the camera very close to the screen. When my Demigod wasn't near battle, I would get 20+ FPS with Fog of War off and Max Demigods; however, when I brought the camera over the Reinforcements fighting my FPS dropped dramatically while the sound was on. When I turned it off the massive drop wasn't so noticable.