Lemma lists represent a necessary tool in NLP. Despite lengthy investigation, I could not locate an Arabic lemma list that would be freely available, and the complexity of Arabic inflections means that the creation of one from scratch is no easy task and should only be undertaken once it is ascertained that none is already available.
I suggest to use wiktionary, say https://en.wiktionary.org/wiki/Category:Arabic_nouns
This resource was used in many projects recently, especially for ones dealing with automatic morphology inflection. Possibly https://ar.wiktionary.org/wiki/%D8%A7%D9%84%D8%B5%D9%81%D8%AD%D8%A9_%D8%A7%D9%84%D8%B1%D8%A6%D9%8A%D8%B3%D9%8A%D8%A9 may be even more suitable.
If you master some tool for HTML processing (I used BeautifulSoup https://www.crummy.com/software/BeautifulSoup/ with Python) you could explore Wiktionary not only to obtain a list of lemmas but also to collect the links to their conjugation tables also available in Wiktionary. It takes time (several hours or days) to write a code which correctly navigates the HTML-structure, however, it certainly worths doing. I used this strategy in my own research on Russian, Latin and Finnish wiktionary.
I think I know of the existence of an Arabic verbal and nominal database but I cannot tell about its whereabouts now. This database inflects automatically any verbal or nominal forms of Arabic. I know about it through IRSIT (Institut Regional des Sciences Informatiques et Telecommunication), where I used to work as a machine translation researcher. This base was attached to the machine translation system in translating from English into Arabic at IRSIT then. Now that the Institute has been sold out (to the private sector, I think) and since this base was developed by specialists in Arabic from Tunisia and France, I suggest that you try to get in touch with Professor Salem Ghazali, who was the director of the project, and Professors Abdulfattah Braham and Joseph Dichy, who directly contributed to the base.
I hope this will help.
This is certainly not an exhaustive solution, but you can get a very substantial list of inflected forms and their lemmas from the Arabic Universal Dependency Treebank:
https://github.com/UniversalDependencies/UD_Arabic
The Treebank contains about 242K lemmatized tokens, so I think those could be collapsed into a rudimentary lemma list covering quite a lot. The license is CC-BY-NC-SA, as shown here:
http://universaldependencies.org/
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