Had similar. The repair is actually fairly easy if you're relatively patient. Square off the hole to eliminate the jagged parts. Take a quick measurement from the lathe to the outer edge of the plaster still there - it looks like its > 1/2" inch so I'll base my next steps on that: Like previous posts have said, get yourself some 1/2" drywall - looks like you might make do with a half-sheet (4x4'), plus get a couple of packs of wood shims, 1 1/4" drywall screws. fiberglass mesh adhesive-backed drywall tape and joint compound (plus a pack of the plastic drywall taping knives if you don't have any). Cut the replacement drywall to roughly match the squared off opening. Then, use the shims in pairs perpendicular to the direction of the lathe to shim out the replacement drywall to shim up the drywall patch to the existing surface of the wall - screw the shims to the lathe with drywall screws and make marks at the top and bottom so you know where the paired-up shims are located. Put the drywall in place and screw the drywall to the shims. Tape the gaps between the repair and existing wall, and finish up the gaps with the joint compound, feathering the compound out onto the wall and repair board to minimize any waviness. Prime and paint.
Sounds like lots of steps but definitely one of the quickest ways to get a relatively smooth repair with a minimum of heartache.