The second spike in the spanish flu epidemic is thought to have started in a US Army camp in southern United states. These soldiers were then shipped over to Europe on a hellish voyage. Huge numbers fell very ill with a much more lethal strain. However they were allowed to disembark and spread along the western front, spreading the disease.
The second spike was bigger because the authorities kept it quiet because they wanted to keep factories open to continue the war effort. As the first wave had ended people started mixing again, and the celebrations of war ending helped maximise the spread even further.
They also did not have antibiotics to help deal with secondary bacterial lung infections.
The mutated second wave of the disease seemed to be more lethal to young fit people (probably creating a more violent cytokine storm) and the war put lots of young fit men in very close proximity.
I wouldn't expect a second peak to be necessarily more lethal, but can we afford to take a chance?