Searching out contemporary accounts of the design and intended meaning of the logo would require going through numerous print accounts and scattered archival collections, but Bill Ayers does refer to the symbol in a 2006 blog post:
Each letter had a logo hand-drawn across the page—our trademark thick and colorful rainbow with a slash of angry lightning cutting through it. New morning, it signified, changing weather. Oddly, as intense as it all looks and sounds, it was in our minds then cautious and responsible, a huge de-escalation from the apocalyptic plans of just months earlier. In any case, I loved that symbol of peace and reconciliation balanced by the hot bolt of justice.
This is tempered by 30+ years of memory, but gives you the basic idea. The lightning bolt is also suggestive of the "single spark [that] ignites a prairie fire," the Mao Zedong quote that inspired the title of the WUO manifesto Prairie Fire: The Politics of Revolutionary Anti-imperialism.