I think they'll do what they did in Gaza. Level everything near the border, destroying buildings, tunnels etc. probably extending up to 30 miles northwards.
Hopefully, the Lebanese will be able to retreat to safer ground. Otherwise, it's going to be another killing field.
There will be benefits for Israel. But there are huge effects for their neighbours and enormous risks of a huge conflagration. Maybe American Christians will think Armageddon has finally arrived!!!