feat(03-03): integrate UDPSender into FastAPI lifespan

- Import UDPSender in main.py
- Start UDPSender on app boot, assign to app.state.udp_sender
- Stop UDPSender cleanly on shutdown (before registry.save)
- All existing lifespan behavior unchanged (beats, registry, show_store)

lightsync/main.py

@@ -7,6 +7,7 @@ from fastapi.staticfiles import StaticFiles
 
 from lightsync.devices.registry import DeviceRegistry
 from lightsync.store.show_store import ShowStore
+from lightsync.protocol.udp_sender import UDPSender
 
 # Module-level containers populated in lifespan
 registry: DeviceRegistry | None = None
@@ -25,9 +26,15 @@ async def lifespan(app: FastAPI):
     # Beat analysis cache: filepath -> {"tempo": float, "beats": [float, ...]}
     app.state.beats = {}
 
+    # UDP sender for device communication (Phase 3)
+    udp_sender = UDPSender()
+    await udp_sender.start()
+    app.state.udp_sender = udp_sender
+
     yield
 
     # Shutdown
+    await app.state.udp_sender.stop()
     await registry.save()