Leonardo ETH + UDP: how?

EthernetUDP-based code compiles, but doesn't run. Works fine with an Arduino Ethernet, and also Uno + ethernet shield.

The Ethernet Shield that connects to the ICSP header should work fine on the Leonardo. What model Ethernet shield do you have?

I'm talking about the Leonardo ETH, not the Leonardo.

The Leonardo ETH uses a W5500 controller. You must use a W5500 library. The standard ethernet library is for the W5100 controller.
http://www.arduino.org/products/arduino-leonardo-eth

Thank you. Why is there an official Arduino product without an official library to support it?

That is only kinda an official Arduino product. It is produced by the people at www.arduino.org, not arduino.cc. Their IDE probably does support it.