Battle of the Lammoth
In The Peoples of Middle-earth, the Dagor-nuin-Giliath took place ten days before the rising of the Moon in F.A. 1, and with the first rising of the Moon, Fingolfin and the second, greater host of the Noldor marched southward into the Lammoth. There they were attacked by Orcs which had been sent there by Morgoth to attack Fëanor in the rear, and they fought their first battle, the Battle of the Lammoth. The Noldor were caught off-guard, and during the conflict Argon, Fingolfin's youngest child, fell. The Orcs made a surprise attack upon the Elves, who began to give way when Argon dashed forward and cut a path to the Orc-captain, whom he slew. The Orcs surrounded and killed Argon, but his brave deed turned the tide of the battle. Fingolfin and his host pursued the Orcs until they were completely destroyed, and then passed into Mithrim as the Sun first rose.
Other versions of the Legendarium
The Battle of the Lammoth and Argon do not appear in the published Silmarillion at all, because they only came to light in very late writings by Tolkien. In the published Silmarillion, Fingolfin's host only arrives after the battle is long over.