Blue lips and fingers could mean that his blood is not circulating as it should. Need to see a cardiologist as soon as possible. There could be something going on with his heart.
There are a few possibilities but first off, I would recommend a second opinion. See if you can get a good picture of his fingertips when they turn color. Has he been seen by a cardiologist or rheumatologist yet? Share the pictures with another doctor and see what s/he has to say. My youngest son got blue lips when he played out in the cold but warmed up just fine. Blue fingertips are something else, especially if it happens at random times.