Small but well-stocked, Lone Pine Sporting Goods has just about anything you would need for a hiking/backpacking trip. Hiking poles, hats, fleece, camping equipment, fishing gear, you name it. It also has a wide range of t-shirts that commemorate the experience of climbing/hiking up Mt. Whitney. If you can't find what you're looking for here, you can try Slater's Sporting Goods to the north about a block. Just go north until you see the big trout sign. You can't miss it!
What to buy: Gear for your hiking/backpacking trip; t-shirt that states you made it to the summit!
What to pay: Varies
Joseph's is the supermarket in the center of Lone Pine. It's small but has everything you would need for your trip up to the Whitney summit or on any other backpack/hiking trail in the area. It has a nice old-timey feel to it and appears to be operated by a single family. We purchased the fixings for turkey and swiss sandwiches here. Also available are various types of energy bars, and just about any other type of food and supply that you'd expect to find in a local supermarket.
What to buy: Food and sundries needed for hiking/backpacking trip.
What to pay: Typical costs for supermarket items.