It would help to explain your need for two different power supplies. Generally you would choose a large enough reg for all the loads, rather than bring in multiple regs.
Sometimes the quality of the Vdd rail isn't good for a combination of digital, analog, and power applications. There's an isolation strategy for every application though.
LCDs don't take much power at all unless you're using a backlight. It seems difficult to imagine that this is going to drag down your supply. Are you sure it's connected correctly?