Lake Kivu has never had a lake overturn but along with Monoun and Nyos it is one of the three lakes in the world which contain such large amounts of carbon dioxide making it very possible that the lake could overturn at some point. The lake is 2000 times bigger than Lake Nyos and has a population of two million people living around its shores.
Professor Robert Hecky (University of Michigan) took samples of the sediments of Lake Kivu which gave a record of the history of the lake going back several thousand years. This showed that approximately every thousand years an event occurred which caused all living creatures in the lake to be wiped out and huge amounts of vegetation to be swept into the lake, which is consistent with a lake overturn.
If the lake was to overturn huge amounts of carbon dioxide would be released, suffocating millions of living creatures, but the lake also contains a large amount of methane which could cause explosions above the lake. Kivu contains enough methane to power the US for a month, and five times as much carbon dioxide – about 200 km3.
In January 2002 the volcano Mount N.. made international news when it erupted, pouring molten lava into the city of Goma in the Democratic Republic of Congo and also into Lake Kivu prompting concern that this would trigger an overturn. The lava has stopped flowing into the lake and the Kivu has remained stable, but after the eruption a crack opened inside the volcano, forming a tunnel carrying lava deeper under the lake. The rift in the area is pulling apart and this will cause the crack to move closer to the bottom of the lake. Huge amounts of boiling lava entering the bottom of the lake would be a huge energy input and would be more than sufficient to trigger a large overturn.
Investigation into how to pipe the gas out of Lake Kivu is currently underway.
Image of lake Kivu borrowed without permission from http://styx.esrin.esa.it/sogha/nyiragongo.html
Image of eruption borrowed without permission from http://news.bbc.co.uk/hi/english/world/africa/newsid_1773000/1773206.stm