||It would be advisable not to. But, it sounds like it already is on the grass. There are two major issues that you need to understand and work around.
1. A person cannot sit on grass on Shabbat or Yom Tov. It is impossible to avoid doing some amount of digging to level out the chair. To rectify this, get plywood and lay it down on the grass. To make sure the seams don't pop up and become a tripping hazard, they sell clips that you put between the plywood pieces that will keep them even.
2. When removing the tarp full of water, you are watering the grass. The only way to deal with this issue, is to take the tarp off right after it rains while the grass is still wet. It is only relevant for one night for you. We only ask for rain in the morning, so you should be safe.
Lots of luck - Hag Sameah