The correct answer is $\boxed{\text{C}}$.
The declination of a star is its angular distance north or south of the celestial equator. The celestial equator is an imaginary line in the sky that lies directly above the Earth’s equator. The zenith is the point directly overhead.
When a star culminates, it reaches its highest point in the sky. If a star whose declination is 60° N culminates at zenith, then it must be located on the celestial equator. When the star crosses the celestial equator again, it will be at its lowest point in the sky, and its altitude will be 60° – 90° = 30°.
Option A is incorrect because the altitude of a star at lower culmination cannot be less than 0°. Option B is incorrect because the altitude of a star at lower culmination cannot be greater than 90°. Option D is incorrect because the altitude of a star at lower culmination cannot be equal to 60°.