The 2 most important reasons for Lions having manes are:
1. Attraction/Reproduction. The bigger & darker the mane, the more the Lionesses like it. The larger mane may also indicate a male who has won many battles, thus is most fit. Males who get beat up most, may lose much of their mane.
2. Intimidation/Protection. The mane makes the male look larger to its enemies (other Lions, Hyenas & such). If he has to fight, the mane blunts damage to its neck & shoulders.
The size and variety of manes can be influenced by habitat; Lions in the hottest areas of Africa have smaller manes, while Lions in cooler parts have larger ones.
Asiatic Lions, in general have smaller manes, despite living in India.
African Lions of the Tsavo region, have little, if any manes at all. Apparently, they are also more aggressive than other Lions.
Lions that live in captivity can grow massive manes because they don't live the hard life of wild Lions. They lack the mental, emotional & physical toughness of "real" Lions, IMHO.
Included is an image of various Lions & their manes. (TOP/Left - Right: African Lion, Asiatic Lion. BOTTOM/Left - Right: Tsavo Lion, Captive Lion.)