Set up your tarp and ladder under the loose plaster. Tap at the loose plaster with the back end of the handle of your drywall knife, knocking down any plaster that will fall. Use the edge of the knife to pry off any other plaster that will come down. The remaining plaster must be solid.
Spread patching plaster over the exposed lath, in a thin layer (about 3/8 inch thick), using your drywall knife.
Rip and press strips of drywall tape into the plaster, lining them up side by side. Cover the whole surface of the exposed lath. Allow the plaster to set for six to eight hours.
Apply a second layer of plaster over the tape, again making the plaster about 3/8 inch thick. Let the plaster dry.
Apply a third layer. Repeat, layering the plaster and letting it dry, then layering it again, until you've build it out to be even with surrounding ceiling surface. Make the final layer of plaster spread out a few inches over the surrounding ceiling at the perimeter of the repair area, blending the new plaster with the old. Let the final coat of patching plaster dry for 12 hours.
Sand the plaster smooth with your sanding pad and sandpaper. The ceiling is ready for repainting.