Do you know if the LCD board has any strange requirements for I2C or otherwise, or if it's a purely 5V board?

I ask because the Omega2 definitely supports all standard 3.3V I2C devices that run at speeds of 100 kbit/s and 400 kbit/s, and our Starter & Maker Kits come with an I2C-based LCD screen, that we know works for sure.

Have you tried powering the LCD screen with 3.3V?