Are you liking the way your pattern is turning out in the yarn you are using? If not, and you haven't had too much time invested in it, maybe you should consider using that yarn for a different pattern and finding a different yarn for your lace.
As for the "furriness" of the yarn and lace, many people make lace scarves and the like out of mohair -- pretty darn furry stuff if you ask me, and even tho you could block a mohair piece, it would still be furry and probably obscure the lace pattern to a certain extent. The blocking would open up the pattern a bit and make the stitches and the piece more even but it would still be furry. So even if you could block the piece, you have to like the effect of the furry yarn on the lace pattern, blocked or not.
Another thing you might want to try is working your lace on a larger needle to open it up a bit. That may help you see your lace pattern better.