The warnings (in 1/2 mile turn left, in 500 feet turn left, in 200 feet turn left) have always been enough for me to realize I need to note the left turn lane upcoming, and move over to it. When there are successive turns, I always get "turn right, then prepare to turn left" to avoid the problem.

I see the opposite problem on one of my regular drives. There are to ramps that turn to the right, about 300 feet apart. I get the "turn right onto..." about 15 feet before the first one. If I didn't know where I was going, I'd certainly take the first ramp an be headed in the wrong direction.