The Lunar Forge can be found in Silent Moons Camp, at the top of the stairs and inside the small barrow.
(Full article: Lunar Weapons)
Furthermore, several Lunar weapons can be found nearby the forge, including under the grindstone.
In order for the Lunar Forge to work, It must be under direct moonlight, thus the name Lunar Forge. A Lunar weapon can be disenchanted and the Silent Moons Enchant learned. This allows the unique enchantment to be applied to other weapons.
Note: Just because it is night time, does not mean the forge is being affected by moonlight.
- The Elder Scrolls V: Skyrim (First appearance)