While lightning strikes are common, most of them occur near the freezing level, and not at flight level altitudes.
Lightning has a mind of its own, and for example will hit wiring in the wing root, as well as the fairing and the fuselage-wing spar joint.
Yes, weather radar is primarily a rainfall detector, and ice is a poor reflector of radar energy. That's why any radar return at flight levels has to be taken seriously. Modern Wx radars are equipped with doppler shift detection, which shows areas of turbulence, if there is the least amount of aerosols to reflect. It will not detect turbulence in clear air.
GB