All the answers above assume the user has access to a privileged/root account to install the required libraries. To install it locally you will need to do the following steps. Only showed the overview since the steps can get a little involved depending on the dependencies that you might be missing
1.Download and Compile libxml2-2.9.1 & libxslt-1.1.28(versions might change)
2.Configure each install path for both libxml and libxslt to be some local directory using configure. Ex. ./configure --prefix=/home_dir/dependencies/libxslt_path
3.Run make
then make install
4.Download and compile lxml from source