Parsing a full site using python
First of all, you should definitely re-use the same session for multiple requests to the same domain - it should result into a performance improvement:


  if you're making several requests to the same host, the underlying TCP connection will be reused, which can result in a significant performance increase


Other Improvements


improve naming: you are over reusing item and titles variables. Instead, think of more appropriate and meaningful variable names. Also, I don't think the "_stuff" prefix contributes to readability and ease of understanding of the program
put the main script execution logic to under if __name__ == '__main__': to avoid executing it on import
you can avoid inner loops and iterate directly over hrefs here:

for link in tree.xpath("//a[@class='sidebar-item-label']/@href"):
    paging_stuff(link)


And here:

for link in tree.xpath("//ul[@class='pagination']//a[@class='pageNumber']/@href"):
    processing_stuff(link)

instead of putting comments before the functions, put them into appropriate docstrings


Notes

Note that you should realize that your solution is synchronous - you are processing urls sequentially one by one. If performance matters, consider looking into Scrapy.