Live there, near Susanville.
Highway 395 Reno to Susanville is good road. No problem in May. Fuel in Susanville is cheaper by about a nickel per gallon at the Diamond Mountain Casino. Main street fuel is higher. No large discount truck stop chains.
Highway 89 through Lassen Volcanic NP will most likely still be closed in May. Highway 44 around the north side of the Park will be open. Same for Highway 36 south of the Park. Both 36 and 44 are kept open year around. Some of the forest roads off 44 will be iffy in May. Count on no fuel on 44 between Susanville and Redding. There is one gas station in the tiny community of Old Station (population 50). May or may not be open, and has tourist prices.
Which campground are you asking about? There is lots of boondocking opportunities in the National Forest around Lassen Volcanic NP. Cell phone coverage can be hit or miss. Mostly miss. Great fly fishing in Hat Creek. Famous for it.
From Lassen Park there is basically three routes to get to Redwoods. Highway 36 from Red Bluff to the coast is not recommended for RVs. Narrow, curvy, not RV friendly. Highway 299 from Redding to the coast is good two lane, but very curvy with a couple of steep grades. I have done it, and is not fun but safe. My preferred route is north on I-5, then Highway 199 from Grants Pass Oregon to Crescent City. Much nicer drive, easier with an RV. This takes you right through Jedediah Smith State Park (Star Wars -- Forest Moon of Endor filmed there) and a nice campground right on the river and next to a large grove of Redwoods.
May in the Redwoods can still be wet and cool in the mornings. Fog commonly burns off mid to late morning, then can be sunny and pleasant in the afternoon. Inland 5-10 miles gets you out of the fog belt and can get hot in the PM.