Use different indexes for Solr searches on local dev environment
Sadly, Solr servers and their settings are not variables. They're not entities, nor anything else Drupal would know about, and subsequently be able to effect.

The settings for the server host/path are stored in a serialised PHP string in the search_api_server table. (the options column).

The best I think you'll be able to do is to add a step to your pull-from-pantheon process to run a script after the database has been updated. The script would perhaps delete all existing servers and add a new record with only the known good configuration for your local host.

Or you could have a module enabled locally only that checks for the host on each request, something like that. I don't think there's a way to do it without altering the database manually, or at least by using one of the API functions provided by search_api_solr.