Hi Matt thanks for posting in the Lucid Community - I'm happy to help! It sounds like you're creating a sequence diagram and Lucidchart has several great templates that might be a useful starting point for you as you model your company's different departments. 

Our basic Sequence Diagram template models a basic process with one actor which you can see in this screenshot below:

I believe you can easily represent multiple actors in any point along your process by placing them along your diagram and extending another dashed line down from them. See another template "Sequence diagram for online shopping" for an example of this:

While this article from the Lucidchart blog is specific to UML sequence diagrams it's a great comprehensive resource on best practices for sequence diagramming in general and may provide helpful guidance and best practices as you build your own.

If I've misunderstood what you're hoping to create please let me know and I'd be glad to continue assisting!