They must be using a lot of power...maybe they are on a weak part of the house grid or whatever. Try plugging your lights in elsewhere? If its happening throughout the whole house, then you need to ask an electrician, there must be a problem there, and you're in danger of blowing the circuit and this could fry lightbulbs or electronics.
The lights and the microwave are on the same branch circuit that may be 15 amps or 20 amps rated. Microwaves require 11 to 14 amps to operate properly and that creates a surge when it's energized, therefore, the lights are momentarily starved of sufficient power and flicker. When the power stabilizes the lights come to full brightness again. All it means is that the microwave needs to be on a dedicated circuit by it's self like the National Electrical Code requires.