As far as I can tell LATA codes are all about 'area' code and the breakup of AT&T. These were created by court order. Anyway, you are attempting to combine/integrate areas (polygons) from two completely different systems, so you're only option will be creating custom polygons.
But before you go to all that trouble, I wonder if you have ALL the current ZIP codes in your dataset? There's a lot more white spaces in your screenshot than I would expect. The next thing to check is do you have the most current list of ZIP Codes (USPS changes/updates them on a monthly basis).
Yes there are some areas out here in the west that don't have ZIP codes (desert, uninhabited areas, etc.) but not sure about your white holes back east.
Anyway, there's probably an LATA shapefile out there that you could probably import as a custom dataset, and then create a polygon map, and then dual axis your ZIP code list on top of that. Lots of work. Lots of limitations. Probably won't be that happy with the results.
My question could be how often does Tableau, or when was the last time Tableau Updated their Zip Code information. I have a list of verified US Zips, and there are about 3000 that Tableau does not recognize. Do we have information on this.