Both a blue moon and a lunar eclipse occur.
A blue moon is an additional full moon that appears in a subdivision of a year: the third of four full moons in a season.
The phrase in modern usage has nothing to do with the actual color of the Moon, although a visually blue Moon (the Moon appearing with a bluish tinge) may occur under certain atmospheric conditions—for instance, if volcanic eruptions or fires release particles in the atmosphere of just the right size to preferentially scatter red light.