Thanks for the suggestion Alan, but the moonroof was definitely closed.
When I contacted the local Lexus dealer, they'd never heard of the problem. However after two or three start/stop cycles, the "gremlin" seems to have disappeared.
There is a slim chance that the beeps had something to do with the "oil change due" warning since the odometer had just rolled over 8,000 km/5,000 miles. I had changed the oil myself at 5,000 km but not reset the warning system. Will post agin if the beeps return.