The English word "lion" may have Semitic origins. Klein, in his Comprehensive Etymological Dictionary of the English Language, writes that lion comes from the Latin leo and Greek "leon" which
is of uncertain, possibly Semitic, origin; cp. Heb. labhi, Akkad. labbu 'lion'
And in his Comprehensive Dictionary of the Hebrew Language, under lavi לביא (a term for an older lion), he says that it is also related to the Ugaritic lbu and Arabic labu'ah - all meaning "lion".
However, Hebrew has more than one word for lion. Let's look at them.
Perhaps the most familiar term (in Modern Hebrew at least) is ari ארי or aryeh אריה. Klein writes that ari is related to Ethiopian 'arwe (=wild beast), Akkadian aru (= eagle) and Arabic 'arwa ( = ibexes). A post on the forum here quotes the HALOT entry for ari, mentions some additional Semitic language with other cognates and animal terms, and writes that the word originally meant "wild animal."
Klein also writes that the word ariel אריאל, which he defines as "hero" and appears only once in the Bible (Shmuel II 23:20), literally means "lion of God" (as does אראל erel - a term for an angel).
Aryeh, Ari and Ariel are all common Hebrew names. The phenomenon of naming people after lions is very widespread as we'll continue to see. The German word for lion, löwe, is cognate with the English, and led to the Yiddish loeb or leib. In Yaakov's blessing to his son Yehuda, he compares him to a lion (Bereshit 49:9). So the names Yehuda, Aryeh and Leib became somewhat interchangeable. In fact, I've seen my great-great-grandfather on gravestones (of his children) mentioned as Yosef Yehuda, Yosef Aryeh and Yosef Leib.
Other biblical names for lions are kfir כפיר and shachal שחל, which along with lavi, are popular Israeli first and last names. Perhaps they gained popularity because aryeh was viewed as old fashioned. Klein writes that kfir - a young lion - might derive from the root כפר, to cover (see this post), and is "properly denoting a lion already covered with a mane".
Two other Hebrew terms for lion are layish ליש and shachatz שחץ, but I have not seen them used for names. (For more discussion of lions in the Bible and in Judaism, see this Encyclopedia Judaica article).
Arabic uses lion terms for names as frequently as Hebrew does. This article discusses the practice, and we'll look at a few examples that have Hebrew cognates.
assad - The Assad family from Syria get their names from the Arabic word for lion, and Hafez al-Assad was known as the "Lion of Syria". (His first name, hafez means "guard or protect" - cognate with the Hebrew חפץ. I recall that in about 1999 a clever Israeli columnist pointed out that the then Director General of the President's Residence, Arie Shumer אריה שומר had a Hebrew name that matched up exactly with the then president of Syria). The Arabic assad is cognate with the Hebrew אשד - a root meaning "to pour" and the source of the words eshed אשד - waterfall and asheda אשדה - slope and waterfall. Klein says the connection to the Arabic word for lion is due to the original meaning of the root being "he rushed, plunged" which became "he pursued" - reflecting the actions of lions
osama - The article gives the following explanation as to the origin of osama:
Meanwhile, the root of Osama/Usama is wasama, which is to brand or stamp (eg, cattle). By extension, wisaam is a mark of distinction or honor and wasaama is grace or beauty—both things that lions have, even if the late Mr bin Laden was sorely lacking in either.
We looked at the same root in our discussion of the etymology of the word monsoon, where we saw that wasama is cognate with the Hebrew shem שם - "name".
abbas - this name for a lion comes from an Arabic root meaning "strict or stern". The Arabic word abasa means "he frowned" (see more discussion here). In A Comparative Lexical Study of Qurʼānic Arabic, Martin Zammit provides us a Hebrew cognate:
Arab 'abasa - 74:22 "Then he frowned and he scowled!": Heb. 'abas: The primary sense is connected with 'contracting' and 'shriveling', with Arab. restricting the usage to the human face and Heb. applying the root to grains.He is referring to the Hebrew root עבש - to shrivel, to grow moldy. This is used in Modern Hebrew in the word עובש ovesh - "mold".
So admiring lions seems to be one thing Arabs and Jews can agree on. Sadly, the Asiatic lion, formerly found in this region, went extinct at the time of the Crusades.