This might sound unorthodox, but what I do when I sit on nice shirts in slightly "off" colors (it sometimes happens with blind buys) is that I bleach the dickens out of them until they take on a nice greige color. I then either use them as is -- greige goes well with autumnal tweeds -- or I re-dye them. If you choose the re-dyeing option, just remember that many shirtmakers use synthetic threads for the stitching, which means that the stitches will always retain their color no matter how much dye you apply.
Well I gave it a shot wearing it as is. It's not as bright as the lime originally pictured but a little louder than my comfort zone is used to. This is indoor fluorescent lighting. Please excuse the wonderfully posed pictures.