As a classically trained musician from very young, I find I usually miss lyrics for the first few times I listen to a piece. I focus more on the instrumental elements of the song--even in non-classical music. Sometimes, I won't actually hear the message of the lyrics for quite some time. I find I have to be consciously concentrating on following the lyrics to process them. A bit strange, I think, but part of how I work.
That said, I always appreciate the music more once I know the meaning of the lyrics behind it--or is that in front of it?