Vacuum cleaners draw a lot of electricity so it's possible for them to dim the lights when you have other loads on the same circuit.
Have you tried plugging the vacuum cleaner into another electrical outlet? If it does the same dimming of the lights on a different circuit then it's likely a problem with your vacuum cleaner motor.
If it only dims the lights on that one circuit then you could have a loose neutral wire in your electrical outlet box or in your electrical panel.
If your lights are only dimming on your living room circuit then you should have an electrician check out your electrical connection to prevent a house fire.