After the failed attack on PLANT homeland on April 17th (intercepted at Jachin Due), ZAFT sought to remove the Earth Alliance from space entirely and destroy Alliance military targets such as Ptolemaeus lunar base and Endomiyon resource base.
On May 3rd, ZAFT forces dispatched to the Moon defeated the Alliance defenders and made landfall on Luna, soon they constructed a base in Lorentz crater to serve as their beachhead. From there, they would continue their offensive on the Moon, eventually dividing the Moon in Alliance-held and ZAFT-held sides, divided by the Grimaldi crater, soon to be known as Grimaldi front.
ZAFT's Lorentz base, from which they base their luna operation from, is in the Lorentz crater on the edge of the dark side of the moon - it can be seen during certain conditions.