The Crisis was the first convergence of timelines, a nexus that occured in the Lost Timelines at an age far before the formation of the Multiverse of Earth 0. A battle started by the power consuming ways of the recently awoken Anti-Monitor, most of the Multiverse of that age was decimated. In the end, the Anti-Monitor was destroyed and the Multiverse collapsed. In the newly formed Sigma Timeline, the effects of the Crisis were visibly seen as it was the only timeline to exist afterwards. Few beings survived the Crisis, with Brainiac doing so by hiding on the original incarnation of Apokolips and waiting out the Multiversal resets.
By the time Convergence came around, the Multiverse was set to break again, but rather permanently, forcing Brainiac to cause the prevention of the collapse of the Multiverse. This did not negate the events of the Crisis on Infinite Earths, as it instead caused time to reset. As a result, the Crisis occured as it originally had and the events of the Lost Timelines played out as intended. The heroes of the Lost Timelines who prevented the collapse of reality, however, instead decided to go their own ways, some making it to Earth 0.