To simplify things, lets call your LWC, component A, and your Aura component, component B.
Currently your components are independent, thus in tree terms, your component B (Aura) is not an ancestor of the component A (LWC).
There are two quick ways you could fire an event from component A (LWC) to component B (Aura)
1) Create a new Aura component that encapsulates component A (LWC). Component A then would fire a standard DOM event and the new Aura component would listen for the event and then re-fire the event as an application Aura event. Component B would then listen for the event and handle it. Something like this gist.
2) Create a child LWC component, call it componentC, in component B (Aura). Fire the event via pub-sub in component A (LWC). Then in componentC, listen and handle your event then re-fire it as a standard DOM event that would be handled by your Aura component, component B.
Events in LWC,
Events from LWC -> Aura