Will a porta potty sink into soft lawn after rain?

Yes, a standard unit can sink or lean on soft lawn after rain if you set it straight on turf with no pad.

We put plywood under ours every time the ground is wet. Two sheets under the skids spread the load so the corners do not punch through. Ask the driver when they call ahead of delivery whether they carry pads. Some do, many do not, so have boards ready yourself. Keep the unit level. A slight lean gets worse once the tank fills and it also makes the door hard to shut.

For the vacuum truck, a firm path to the unit matters as much as the pad under it. Soft lawn takes ruts fast on a service visit. If the hose can reach from the street you already have that part covered. After a heavy rain, wait a day if you can before they drop it, or lay the plywood the morning of and leave it under for the whole rental.

Carl is right about plywood. One thing I would add from wet-lawn drops: use at least two sheets under the skids and keep them wider than the unit footprint so the corners cannot punch through when the holding tank fills. A single narrow board under the middle still lets a corner dig in after rain.

Ask the driver to set the standard unit level with a phone level or a visual check on the door gaps before they leave. A small lean on soft turf gets worse over a week. If the lawn is already mush Monday morning, wait a day if the remodel allows, or lay the boards the night before so they settle flat.

For the vacuum truck, confirm the hose path from the street stays on firmer ground (driveway edge, plywood path) so they are not spinning tires on the wet grass during the service visit. We kept a remodel unit on lawn through a wet spell that way with no tip and only light marks where the boards sat.