You'll see a few pullouts around Otis (mini-town just east of LC). There's access near the hatchery, too. Actually, you'll find places all up the river.
I haven't fished there in years (even though I spent many months working in LC, not sure how that happened), but it's my understanding that hatchery fish are few and far between on the Salmon. You could drive the extra 15-20 minutes to Pacific City or Hebo and hit the Nestucca, which might be better fishing.