I'm assuming you mean either the Kings Range (between Shelter Cove and the Mattole River), or the Sinkyone State Wilderness Wilderness State Park (Shelter Cove south to Usal).
Gear needed for this trip is nothing extraordinary. This time of year, you'll end up with fog and potentially some wind, but I can't imagine lows below 50 or highs above 80 at the absolute, absolute max (assuming you stay on the coast). I'm not sure what the freshwater availability is up there right now, but I often find that that water is frequent enough that I get by tanking up at stops and carrying no more than a half liter of water at a time. Bugs won't be too bad. If you do the Sinkyone, you'll end up brushing up against a lot of poison oak. I'd recommend long pants, and if you're going to be more than a day or two, biodegradable soap so that you can wash the oils off of you. So, my recommendations would be:
A wind-tolerant, but well ventilated (b/c of fog) shelter. You'll have more options if you can pitch it on sand, so you'll need either extra guylines that you can tie around driftwood, some fat stakes, or a freestanding shelter. I often camp on the beach with just a groundcloth, but the wind can pick up.
Clothing that gives you a few light layers to play with, but no need for high-loft clothing. You should prepare for fog and wind, but I often go without raingear of any kind.
A bear can (required for the Kings Range, not a bad idea for the Sinkyone; can rent when you get your Kings Range permit).
For the Kings range, whatever footwear you need to be comfortable with mild stream crossing and/or dancing in and out of the tide (I usually just go barefoot for crossings there). For the Sinkyone, unless you have very strong ankles, it can be a good idea to wear hiking boots even with a UL load.
Stove: on the beach sites (all along the coat trail in the Kings Range, most of the Sinkyone), there's typically plenty of driftwood cookfires if you want to take that route.
The rest, and how you meet the above, is pretty much up to you. Any of the three-season sierra gear lists on this site will work. I find the lost coast to be an especially forgiving place to camp in the summer, unless you are particularly skittish about poison oak.