Does anyone ever find themselves in a situation where you need to delegate a task laterally, instead of down to a direct report? Curious how others handle having to make a request where success depends on needing to rely on a peer outside IT.

I would be surprised if this isn't a common task for IT leaders.  We often need our business partners to work with us to deploy the systems they need and to help support the systems we need.  I wouldn't think of it as delegating but would ask them to partner with you in the project identifying for them what is in it for them, ie how the outcomes benefit their department or the organization as a whole.  

To me, delegation CAN mean telling someone to do something when in this case you need to ask.  

as an IT Director in a municipal environment, I often find myself in this situation. Many of our digital transformation and cybersecurity initiatives require strong cross-functional collaboration, where I need to delegate tasks to peers outside of IT (legal, communications, citizen services, finance, etc.). In these cases, I rely on a partnership-based approach: I make sure to clearly communicate the strategic context, articulate the shared goal, and recognize my colleague’s expertise. This helps foster engagement and mutual trust, even without a formal reporting line. In my experience, influence and clear communication are far more effective than hierarchy in these scenarios.