From The World of Ice and Fire, it seems as though the author, George R. R. Martin, and his co-authors (Elio Garcia and Linda Antonsson) want us to believe that it was one of Lann's descendents, given that he was titled posthumously:
Lann the Clever never called himself a king, as best we know, though some tales told centuries later have conferred that styling on him posthumously. The first true Lannister king we know of is Loreon Lannister, also known as Loreon the Lion
-The World of Ice and Fire: The Westerlands.
From the main books, I think GRRM wants us to believe that it was Lann The Clever who was the first Lannister. Or at least Lann's first immediate descendent (being that they would have been a Lannister.
From A Game of Thrones:
He opened to the section on House Lannister once more, and turned the pages slowly, hoping against hope that something would leap out at him. The Lannisters were an old family, tracing their descent back to Lann the Clever, a trickster from the Age of Heroes who was no doubt as legendary as Bran the Builder
-A Song of Ice and Fire: Book One - A Game of Thrones, Chapter Twenty-Seven (Eddard VI).
And from A Storm of Swords:
“Your place.” The voice echoed; it was a hundred voices, a thousand, the voices of all the Lannisters since Lann the Clever, who’d lived at the dawn of days.
-A Song of Ice and Fire: Book Three - A Storm of Swords, Chapter Forty-Four (Jaime VI).
And from A Feast For Crows:
The Lannisters of Casterly Rock remain the principal support of King Tommen’s claim to the Iron Throne. They boast of descent from Lann the Clever, the legendary trickster of the Age of Heroes.
-A Song of Ice and Fire: Book Four - A Feast For Crows, Appendix.