I can't find a decent documentation on how to make updates to solr using pysolr.
You cannot currently make atomic updates to Solr using PySolr. There is a pull for it:
https://github.com/toastdriven/pysolr/pull/99
But it's not yet been merged. Last comment was less than a month ago, if you are interested I'd comment on it - or try to merge the code yourself if you feel up to it.