AFAIK, there isn't a way to translate Zipcode
to Lat/Long
in Solr.
Most Geospatial queries (not restricted to Solr) use Latitude and Longitude to perform a radius search. So this isn't a Solr specific problem.
I would recommend enriching the data that is imported into Solr using a GeoCoding API.
You can update your existing index to have these fields populated for every document, but if possible I would prefer recreating the Solr Index with this data.
I wouldn't include another collection for this purpose, JOIN isn't supported in Solr, as it isn't a relational data store.
Edit: Solr does support JOIN, but in your case I would still not go for it, unless I have to.