What do you think are the major imports to Lannisport/Casterly Rock?

That’s a good question. I’m guessing there’s a fair degree of food imports (mostly from Reach, Riverlands) – the Westerlands are pretty hilly, which tends to mean less arable in terms of grains and vegetables (Westerlands seems to tend more towards cattle-herding). Wines, definitely, both from Dorne and the Reach. Wool and probably timber from the North, tin from the Isles, linen or flax from the Reach, Dornish silks and citrus fruits and olive oil. 

Lots of luxury goods from Essos, I imagine – chiefly textiles (lace, tapestries, carpets, fine woolens), but also perfumes, dyes, spices, advanced manufactures from Myr, furs from Qohor (I’m guessing there’s a heavy tariff on steel to protect strategically important industry), hard alcohol, glassware, etc.