This algae lamp idea is a bit of a strange story. If you watch this 2013 TedX video, at 9:35 you see what seems to be algae in a tank giving light. However, never in the video did the inventor use the words 'algae lamp' or did he say that the algae are providing energy. Instead he says that he wants to use these street lamps for carbon sequestration, so the algae are not for lighting! I suspect in the movie they use an external light source to provide light to the algae (they need light and CO2 to grow).
According to this page in 2007 Pierre Calleja patented an idea about an algae lamp where a battery would be charged via photosynthesis. However,
If you search the inventor's company website for the keyword 'lamp' you get 0 hits. This all leads me to believe that they first tried to develop algae lamps but failed and are now pursuing a different approach and that is using algae for carbon sequestration.
I was able to find a paper that describes how scientists from Stanford University and Yonsei University in Seoul managed to attach the gold electrodes to the
cells of an algae. Unfortunately I don't have access to the full paper, but this 2010 Stanford news release provides some additional information:
The Stanford research team developed a unique, ultra-sharp nanoelectrode made of gold, specially designed for probing inside cells. They gently pushed it through the algal cell membranes, which sealed around it, and the cell stayed alive. From the photosynthesizing cells, the electrode collected electrons that had been energized by light and the researchers generated a tiny electrical current.
The news article also describes the problems:
...they were able to draw from each cell just one picoampere, an amount of electricity so tiny that they would need a trillion cells photosynthesizing for one hour just to equal the amount of energy stored in a AA battery. In addition, the cells die after an hour.