I don't believe so. Please check out the following paper for the issues involved in developing such corpora: http://archimedes.fas.harvard.edu/mdh/arabic/NAACL.pdf.
Hi, it is not so bad, but depends how you specify free.
The Prague Arabit Dependency Treebank that includes manual morphology is distributed under CC-BY-NC-SA license: http://hdl.handle.net/11858/00-097C-0000-0001-4872-3. It was also published in a format harmonised with other treebanks here: http://ufal.mff.cuni.cz/hamledt, that version also costs nothing.
If you want to have a look at the data online before downloading, you can directly search the HamleDT (harmonised) version in a traditional "keyword in context" way here: https://lindat.mff.cuni.cz/services/kontext/run.cgi/first?shuffle=1&reload=1&corpname=hamledt_20_ar_a or in a tree-search way here: https://lindat.mff.cuni.cz/services/pmltq/hamledt_ar/
the Sketch Engine (http://www.sketchengine.co.uk) contains a 115M web crawled corpus (sample or arTenTen) that is both lemmatized and part-of-speech tagged. The former is much more problematic than the latter for Arabic, actually -- if you just need the tagging then there is Stanford Arabic Tagger integrated into Sketch Engine so whatever data you upload will get tagged, and there are more Arabic corpora already present that are tagged but not lemmatized in the system. The data is not immediately available for download but if you would need that please drop a mail to [email protected] and we can discuss that.