Lights shouldn't be dimming throughout the house. Especially not LED. They should only dim if they're on the same circuit.
A breaker isn't always going to trip from an amp. Lots of transient power requirements. It takes constant overload to trip a breaker.
I'm guessing the amp is on a 15 amp circuit? If you go by code, constant power draws should be 80% of what a breaker is rated for. So if that amp is drawing 12 amps, that's all code rates that circuit for.