DCI: Last Alliance is a submod for Third Age: Total War, focused on the War of the Last Alliance in the Second Age of Middle-earth.
Lothlórien begin with three regions; Cerin Lóri and Caras Galadhon in the ancient forest itself, and the haven of Edhellond next to Gondor, at the bay of Belfalas.
They have the haven near Dol Amroth?
Yes, it's the haven of Edhellond.
Originally founded by some Sindar from Beleriand, in the late First Age, they were mingled with and Edhellond became mainly inhabited by Silvan Elves from Lothlórien, during the Second Age.
Later in the Third Age it was depopulated as Elves left for Valinor. The last ship that left had Lórien's king Amorth onboard, but he drowned (tragic story); possibly why Dol Amroth* was named as it is in latter days.
*In DCI:LA there's a small fort at that place, but named Dol Belfalas. The Prince of Belfalas (in later time known as princes of Dol Amroth) live in Tarnost further inland in Belfalas.