I have heard of folks making "grass tea"... soaking fresh-cut grass in water for several hours, and then using that water on the plants. I've never tried that myself. Grass is relatively high in Nitrogen, but I don't know if much of that (N) would actually make it into the soil when the grass is applied as mulch or watered-in.
Also, keep in mind that most (County Extension) soil tests don't even bother to try to test for Nitrogen because it is volatile or "fleeting". In other words, by the time the soil sample is removed from the ground and gets to the lab for testing, the nitrogen measured may not be indicative of the actual levels available "in the ground".