Hey Dan,
First, welcome! Glad to have you here as a new maker.
Second, if your issue isn't related directly to GCC/High/DoD, I would recommend using the regular maker's forum for questions. You'll get faster response from the wider community.
For your issue, you don't need two lookup fields. I would first, try creating a calculated field and use the first lookup to populate the calculated (email) field. If for some reason that doesn't work, you can leverage JS to populate a text field or a flow (Power Automate). The latter will not populate in real time though, so the UX may not meet your needs.
But again, try the regular forum and you might get other options.