Power green LED from microbial fuel cell (MFC)
Okay, here are some considerations.


Your source has the energy storage of 0.6V* 0.2 mA * 1hr = 120 uW-h.
If you get some newer LEDs, say LTST-C193TGKT-5A chip LED from Lite-ON, it has a fairly high efficiency, about 100 mcd at 5 mA., not the miserable 7 mcd @ 20 mA as for GNL-3012GD, or 50 times more efficient. I just run a test, so the light is pretty visible at 16 uA (micro Amp !!!), with forward voltage about 2.3V. This equates to power consumption at just 37 uW, while you can see the light with no mistake. If I take a proportion of 100 mcd and 16/5000, this is about 0.32 mcd of light, and there are many LEDs with 0.1 - 0.3 mcd light output. So the 0.32 mcd is pretty visible.
Now, if you find some "energy-harvesting" IC operating at 500-600 mV, with output boost to 2.3-2.5 V, something like the module from Advanced Linear Devices, or LTC3108, the LTST-C193TG LED will be glowing (at 0.32 mcd) for up to 3 hours.


The hints here are (1) high-efficient LED, and (2) energy-harvesting IC.
Would it fit your requirements?