According to the journal of Abbess Germaine, Lake Kotir began to dry up when Wuddship was resurfaced, because the River Moss regained its natural flow and the flood tunnels were reduced to a trickle (and then dry, as stated in The Long Patrol). The lake was reduced to a spring-fed swamp. A drought after that brought the swamp down to just the pond in its middle, and the places where marsh used to be dried out. The Redwallers-to-be incorporated this in their plans as the pond, and Redwall was finished with it in.
As Lake Kotir
When Mossflower Woods was newer, the River Moss had a different course than it did during the time of Redwall. The curve it took by Kotir was once broader, likely going through the valley that Kotir and Redwall were/are in, forming a lake. Later, the river changed course due to unknown reasons, and the lake was no longer part of its course. After years, it dried out, the drainage becoming the The Gloomer's cave. The creatures that originally build Kotir used the valley to build it. Later on, the creatures left it probably because it was crumbling and they couldn't take care of it, and Verdauga Greeneyes found it. His daughter Tsarmina Greeneyes took it over after his death, and the Corim eventually used the flood tunnels and Wuddship to recreate the lake and flood Kotir.
As the Swamp
After the Wuddship was resurfaced, the river regained its natural flow, the flood tunnels were no longer draining water into the underground ruins of Kotir. (this is why the flood tunnel method could not be used on Redwall, because the ground level apparently rose with the lake, and Redwall was built above Kotir.) Because of this, the lake dried up, and only remained as a swamp in the premises of the Redwall building site. At the swamp's center was a spring-fed pond. In the middle of Redwall's construction, a dry season hit Mossflower, and the swamp dried up into dry land, leaving only the pond behind.
As the Abbey Pond
When Redwall was finished, it had a pond in its grounds. It has been mentioned in all the books with Redwall, most notably in the times of Blaggut, Matthias, Alf, Fermald the Ancient, Grimjaw, and more. Dibbuns go there to swim in the shallows, and often otters go there too.