In “The lands of Ice and Fire” it is shown that there is a river right next to Casterly Rock that goes inland. It flows into a valley with no mountains, and in this same valley is the Tumblestone River. Therefore, what you would think of a canal linking these two rivers? Like the Hornvale-Red Fork canal it would severely shorten the trip from the Westerlands to the capital, but with House Lannister gaining direct benefit. This would also connect Lannisport (a few miles away) to the capital.