Why not just build a wall as a sound barrier to push the noise upward and over the bike lane?
I do not think a freeway-adjacent bikeway would be popular with cyclists if open-air. LA has a freeway-adjacent bus rapid transit line (the "Sliver Line") which isn't very popular at 12K avg boardings in March 2013, compared to the far more successful rail-route-replacing "Orange Line" at 30K+ avg weekday boardings for the same month.
The Orange Line has a parallel bike lane which is popular with cyclists and pedestrians, even into the evening as it's well-lit and well-landscaped.
Edit: Reference for LA Metro system boardings: http://www.metro.net/news/ridership-statistics/