GURREN-LAGANN IS GILGAMESH MEETS GETTER ROBO. Just look at the second arc, and the obvious comparisons:
In The Epic of Gilgamesh, Gilgamesh is a powerful king (indeed, undefeated, no one on earth can withstand his might) who's domain has become corrupt. Enkidu is a wild man, formed from the earth by the gods in answer to the cries of the people. In the Epic they send Enkidu to the city, so that he can kill Gilgamesh, but in the end Gilgamesh wins the fight, yet respects Enkidu as an equal. Together they go to face the demon Humbaba (notably weilding swords weighing 150lbs a piece... which is where the sheer immensity of the mechs actually becomes a valid comparison for the scale on which these epic heroes operated).
In Gurren Lagann we have Viral, described as a "beast man", part human, part animal, a clear reference to Enkidu's bestial nature. Savvy Gurren fans will at this point have spotted that Enkidu is also the name of Viral's mech, an obvious tip of the hat by Gainax. In the second arc he reappears, ferrying the citizens of Kamina city back to safety underground. As in the Epic, he has been sent by the gods to answer the prayers of the people, and to challenge Simon, our analogue for Gilgamesh, breaking him out of his comfort and safety, and forcing him to face his own corruption, in this case split off into the character of Rossiu.
In the Epic of Gilgamesh, Enkidu's role is to eventually die, spurring Gilgamesh to be begin his quest for eternal life. In Gurren Lagann, this part of Viral's role has already been fulfilled by Kamina, whose death ushers in the arrival of Nia, Simon's quest for the latter part of the series. Just as with the Epic of Gilgamesh, this quest is ultimately hopeless; just as Gilgamesh fails to achieve eternal life, despite seeing that it is possible, so Simon never truly possesses Nia, as she too fades from his grasp.