I would like to ask if there is any module for recommendations (products,nodes etc) based on Solr.
I have searched on Drupal.org, and I have found Content recommendation modules, which doesn't list any module using Solr.
Actually, if you go to Apache Solr's 'Pages/blocks' configuration page at admin/config/search/apachesolr/search-pages, you should see whether your "More like this" (which is like a "Related content") block is enabled.
If it's not, just click on the "Add search block "More Like This" as shown below:
That will take you to a page where you can configure your 'More Like This' block.
Would this default block that comes with Sorl meet your needs?