The brain signals were even sent over a standard internet connection to drive a second robot arm in a different laboratory.
Sensors mounted on the machine send "visual" signals to the lamprey's brain which, in turn, transmits instructions to the robot's motors.
Scientists at Northwestern University, Chicago, US, developed the system to study how human and animal brains control movement. The intention of this, and similar, research is to learn lessons that will aid the development of better artificial limbs.
Professor Sandro Mussa-Ivaldi, whose team developed the fish-machine interface, said: "This is trespassing on nature but scientists do that all the time. It's worth it if it leads to new knowledge and better prosthetic limbs."
Researchers believe that in the future robotic arms and legs will be wired directly into, and controlled by, the brains of individuals whose own limbs have been lost because of accident or disease.
Internet connection
This month, researchers showed how a robotic arm could move in three dimensions and in real time using the brain signals of an owl monkey.
The movements in the machine mimicked those of the animal's own arm as it reached for food on a tray.
The brain signals were even sent over a standard internet connection to drive a second robot arm in a different laboratory.
Scientists have also wired a mechanical water feeder into the brain of a rat. At first, the animal would move the device towards its mouth by pushing a lever. But eventually, the rodent learnt how to bring the feeder closer by merely willing it to happen.
The Science Museum display features a robot and lamprey similar to the ones used in the Chicago research. It also includes a video of the robot in action.
The display is part of the Antenna exhibition in the museum's new Wellcome Wing. Antenna is updated on a monthly, weekly and even daily basis, presenting the very latest science and technology news to museum visitors.