Start watering it soon. Put out some cat food or tuna cans and turn on your watering system (sprinkler or in-ground). Watch for the cans to fill up and time how long it takes. That is your baseline for watering. Water it that long once per week. Then mow every week. Watch for seed heads to form on that coarse grass and take some close up pictures. Get the camera about 3 inches from the grass. Seed heads make it much easier to identify a grass. The time to renovate would be in late August for you in NH. It is also the time to overseed with fescue seed if you have that. The color leads be to think you have Kentucky bluegrass. Grassy weeds, like what you seem to have, are hard to get rid of in a grass lawn. It usually requires renovation where you kill the entire existing lawn and put down new seed.

I was planning to fertilize and overseed soon. There's one area with very little good grass that's now completely covered with crabgrass. I do need better soil nutrition there, but also more good grass seed. I'm thinking now I'll try to weed whack the crabgrass where it's thick before I overseed to allow for more seed/soil contact. I figure it would be useless to overseed on it as thick as it is. I try to stay mostly organic so I've never used pre-emergents..

Seedheads do not look correct for Saccharum. Also a little too compact for ravenna grass as well....it can easily grow to 8-12' tall. I'd suspect some sort of Miscanthus but it is too indistinct and crowded to nail down a specific variety.

Really need to see a seedhead. btw, both zoysia and fescue go dormant - zoysia in cold weather (below 50F) and fescue in summer (unless watered heavily to prevent). Of the two, fescue is the most shade tolerant - zoysia does best in full sun.