The Short Version
This claim is true. Cleopatra died in 30 BCE, roughly 2,000 years before the 1969 moon landing. The Great Pyramid of Giza was completed around 2500–2570 BCE, placing it roughly 2,450–2,540 years before Cleopatra. Since the gap to the pyramid is consistently several centuries larger than the gap to the moon landing, Cleopatra indeed lived closer in time to the Apollo 11 mission than to the construction of the Great Pyramid.