The Solr requirements can be found here: https://wiki.apache.org/solr/SolrInstall
So an installed JRE is needed, but also an servlet container, which also needs an JRE.
If I would be in your situation, I would rent an virtual server. An other option is an hosting service, specialized for solr hosting: search the web for “apache solr hosting”. There are offers for free or payed offers also.