What is the best way to have a lookup that supports creating a new record if one isn't found?

Ok got it -
Add a new model for SingleLender, clone your Lenders model, but uncheck load on page load
your row action on New Submissions opens the popup like you have it
The popup has your table of Lenders. Your row action for each lender does the following:
Adopt Rows into Model - source: Lenders destination: SingleLender
Close Popup

In the popup, add an After-close action of Update field on row just like you did before, update the NewSubmission Lender__c field, but choose Single Specified Value, then put in {{$Model.SingleLender.data.0.Id}}

Should work. On your row action to open the Lenders table, you’ll also want to remove all rows from Single Lender model, so you’re clearing it out each time. 

And it works if you create a new lender and don’t save it, but works better if you save the new Lender first, so on your close action or row action you might add a save Lenders model somewhere

I’ve got a prototype page if any of that is confusing