The word "limelit" is an adjective form of the noun "limelight". Many years ago, in the early days of stage theater, a limelight was a type of lamp used in stage lighting, in which light is produced by heating lime to white heat. That kind of lighting is no longer used, but the idiom "in the limelight" derives from it, which is to be in a position of public attention or notice (as were the performers on those stages in days gone by). So the speaker in this paragraph is someone who is well known; someone who is "in the limelight" in his public life. Thus the air around him when he speaks is "limelit air".