BeautifulSoup is a Python package that parses broken HTML, just like lxml supports it based on the parser of libxml2. BeautifulSoup uses a different parsing approach. It is not a real HTML parser but uses regular expressions to dive through tag soup. It is therefore more forgiving in some cases and less good in others. It is not uncommon that lxml/libxml2 parses and fixes broken HTML better, but BeautifulSoup has superiour support for encoding detection. It very much depends on the input which parser works better.
To prevent users from having to choose their parser library in advance, lxml can interface to the parsing capabilities of BeautifulSoup through the lxml.html.soupparser module. It provides three main functions: fromstring() and parse() to parse a string or file using BeautifulSoup into an lxml.html document, and convert_tree() to convert an existing BeautifulSoup tree into a list of top-level Elements.