Actually you do have reason to be concerned, especially if the broken lip is still on the car and if the carbon fiber lip actually has any carbon fiber in it and not just a carbon fiber appearance.
The air that the lip directs up into the engine compartment exits just behind the hood at the base of the windshield. This is where the outside air comes into the interior of the car through the cabin air filter.
The problem is that if the lip has true carbon fibers in it, the filter will NOT stop them. They are way too small. They are not as bad as asbestos because they don’t get lodged in the lungs the same way, but they do irritate the lungs and with constant exposure, they can do the same damage.