High-frame-rate X-ray pixel detectors make it possible to perform time-resolved experiments at synchrotron beamlines, and to make better use of these sources by shortening experiment times. LAMBDA is a photon-counting hybrid pixel detector based on the Medipix3 chip, designed to combine a small pixel size of 55 µm, a large tileable module design, high speed, and compatibility with "high-Z" sensors for hard X-ray detection. This technical paper focuses on LAMBDA's high-speed-readout functionality, which allows a frame rate of 2000 frames per second with no deadtime between successive images. This takes advantage of the Medipix3 chip's "continuous read-write" function and highly parallelised readout. The readout electronics serialise this data and send it back to a server PC over two 10 Gigabit Ethernet links. The server PC controls the detector and receives, processes and stores the data using software designed for the Tango control system. As a demonstration of high-speed readout of a high-Z sensor, a GaAs LAMBDA detector was used to make a high-speed X-ray video of a computer fan.