It is not the issue of carbon-fibre but to be certified, it must demonstrate the ability to take strikes without negative effects. Lightning is considered part of the operating environment, like ice, and thus for the airplane to achieve FAA and JAA cert, it must pass lightning certification.
WIth carbon fibre airplanes, often manufacturers will embed mesh into the structure to help keep the lightning on the surface and to bleed it away from the more critical components. Also, things like computers and such are put in hardened sites to protect and shield them from strikes.
Interesting is to learn there are Negative Strikes and a Positive Strike, not that you have any choice. But the Positive Strike (singular) is estimated to be about 10 times more powerful than the negative strikes (plural)
When you land, if you have pitted surfaces, it was negative. If you have parts missing, it may have been a positive.