There have been people congregated around the Lake and in that area for thousands of years, For a while it was the most densely populated areas of Africa not on the coast. As far as named, and internationally recognizable civilizations go, it is hard to name civilizations that started there. There has been the Kitara Kingdom, found here; http://www.bunyoro-kitara.org/7.html . The Kitara Kingdom, especially under the Bachwezi dynasty, was as far as any linked together Civilization around Lake Victoria ever came to being a major player. But Like i said, these never became continental powers and were constantly broken up by nearby raiding tribes, which is why they are seldom studied unlike bigger African tribes like Songhai.

Counterfactuals go in /r/historicalwhatif , if memory serves. But offhand I can tell you that Nalubaale/Victoria is not exactly useful water the way temperate glacial lakes or seas are; it's got a number of parasites (notably bilharzia/schistosomiasis) that involve humans in their life cycles, attesting to our co-evolution in the region. Fishermen do well, though.

But there have been a great many states in the interlacustrine region. Buganda is perhaps the most notable that's survived, with a Kabaka back on the throne. But Jean-Paul Chretein's Great Lakes of Africa goes much further back; Chris Ehret's An African Classical Age talks about the dynamism of that region and its cultural and social interchange up to 1000; and David Schoenbrun's A Green Place, a Good Place deals with the earlier complex civilizations up to the 1400s. Start there, and realize that we've only really scratched the surface in terms of the deeper oral and material evidence for the antiquity of complex state formations.