As already mentioned, I would use a piece of Sheetrock to fill in. I would add a couple of points:
You'll want to use mesh tape on this. Plaster is portland cement based, meaning it likes to absorb water. The mesh tape will hold up better compared to paper tape here. I'd also look for the rot-resistant sheetrock for the same reason.
Secure or remove the loose plaster behind the sheetrock before patching. Ideally, it would be best to get the sheetrock to rest only on the lath. I'd even run a bead of construction adhesive between the lath and sheetrock (along with screws).
For patching plaster, I've used the following procedure with very good success. This assumes good attachment to the lath. If the plaster keys are broken/loose, then that requires some more attention. Crack repair also needs dug out before repairing.
Remove any loose or soft plaster pieces. Vacuum out the area to be repaired. Use something like Elmer's Glue-All and mix 50/50 with water. Using a brush, apply the glue mixture to the old plaster that will be repaired. Again, the reason for this is the plaster likes to absorb water. The glue mixture will help seal the old plaster so that it doesn't take the water from the repair material and also aid in adhesion. Mix up some Durabond 90 for the base patch. Durabond is very strong but it is not intended to be sanded so make sure it is not proud of the finished surface. As a side note, Durabond or other drywall compound that comes in powder form is (almost?) always a setting compound. This means is actually cures like concrete rather than simply dry out like the pre-mixed joint compound. I think it's generally understood that setting compound is stronger than pre-mix. I recommended Durabond 90 as the 90 means it sets in 90 minutes. The longer the set time, the stronger it usually is. Once the Durabond is mixed, try to apply it to the repair area while the glue/water mix is still a little tacky. Allow this to set before applying "sandable" joint compound.