On a recent Saturday afternoon, a radar operated by French United Nations peacekeepers picked up a pilotless Israeli reconnaissance drone crossing into south Lebanon. It was given no more attention than any of the dozens of other surveillance missions flown by the Israelis in Lebanese airspace each month.

But when the drone passed above Wadi Hojeir, a yawning valley with steep, brush-covered slopes, it abruptly vanished from the radar screen. The startled peacekeepers contacted the Lebanese army,...