I need to leave something on the lawn for a few days, and I wonder if
there is a way to avoid damaging the grass. And how long it takes to
start killing the grass. And what the best time of year is for this.

The easiest way to remove my small deck, 4' x 8' that is falling
apart, seems to be to get a bagster www.thebagster.com and put the
wood from my deck in it. 30 for the bag and iirc 130 to have it
removed. (Not the cheapest but the easiest.) 4'wide x 8'long x 2.5'
high, the entire top is open, and it will hold 3300 pounds, they say,
but the 350 or 500 feet equivalent of 2x4 won't weigh anywhere near
that much. How much does a 2x4 weigh per pound? Half are pressure
treated and half aren't. (It will hold 180 8-foot 2x4s and I don't
have more than 70's worth.)

But they don't want the thing on the street, even in the parking lane,
only in the yard or driveway and I have no driveway. I had surgery a
couple months ago and it will take me say 2 days to put all the wood
in it, and it will take them 1 to 3 days to pick it up, they say. So
3 to 5 days total.

The bag is I think polypropylene, not a tight weave, so air will get
through. The end of the first day the bag will be only half full.

Is there something I could put under the bag that would help the grass
underneath?

How long before the grass starts to die?

Does it matter what time of year, how cold out it is? I have more
surgery at the end of January so December/January would be good for
me. If not then it may have to wait until June.