Question
Can I spread cow manure or mushroon compost on my lawn?

Answer
Yes you can but...compost is a great soil amendment to help improve the texture of your soil.  It is not a substitute for fertilizer.  Once composted, there is very little, if any, nitrogen left in it and turfgrass needs a good bit.  The other downside is compost often contains fungal spores.  The combination of decomposing organic matter and fungi may lead to some lawn disease issues. You'll benefit you lawn more with a good fertilizer and maintaining a proper pH.  Jim