Ever since Lann the Clever took Casterly Rock from the Casterlys, the Lannisters have ruled over the westerlands, first as kings, and then after the Targaryen conquest, as lords in service to their new king. The importance and influence of the Lannisters has grown in the last quarter century since Tywin Lannister came to power and restored the house to its proper glory.
From “A Song of Ice and Fire Campaign Guide”, Page 166
The current status of House Lannister
House Lannister of eleven years prior to “A Song of Ice and Fire” book series is somewhat different than readers or watchers are used to. At this time, here are the differences: