You can get a string from the element and then write that from lxml tutorial
str = etree.tostring(root, pretty_print=True)
Look at the tostring documentation to set the encoding – this was written in Python 2, Python 3 gives a binary string back which can be written directly to file but is probably not what you want in code.
or convert to an element tree (originally write to a file handle but either missed when I wrote this or it is new it can be a file name as per this answer )
et = etree.ElementTree(root)
et.write('output.xml', pretty_print=True)