Lax-C, 1100 N. Main, near Chinatown in downtown, is the Thai market where most of the local Thai restaurants do their shopping. It is open to the public and is a remarkable experience. Easily as big as a Costco, with an enormous variety of every kind of food, produce, meat, seafood, fresh items, canned and bottled items, spices, herbs, as well as kitchen equipment, housewares, sundries, you name it. All Thai. A good cheap food court, too. It is much cheaper than any of the other Thai markets in town, with a much more extensive selection. I highly recommend it.
Exactly what I would have said but you beat me to it! While I usually shop at Bangkok Market in L.A. or one of the 2 Bang Lucks in the SFV when I just need a coulpe of fresh produce items or whatever; LAX-C is by far the best best on selection, price, ready to eat food vendors and the overall "wow, am I really in L.A. experience!" If you need a lot of stuff, LAX-C is the best.
Note, I tried but did not succeede in linking to the Bang Luck Markets.
1100 N Main St, Los Angeles, CA
Bangkok Market Retail
4757 Melrose Ave, Los Angeles, CA