Since that sawdust is organic matter it can be raked into your turf, but next year you may have a bumber crop of mushrooms there and that does bother some people even though they are not a problem. I would do nothing more than I normally do in that area, especially I would not put down extra highly soluble Nitrogen that could "burn" the grass.

try soybean meal, cottonseed meal or alfalfa pellets to speed up the decomposition of sawdust.

I appreciate the feedback here. I don't mind mushrooms all that much since I've heard they're a sign of a healthy soil. And it's just about time to do an application of soybean meal anyway, so the timing's pretty good.

Best regards to you both.

-Ray