Blue & Gold's post was spot on.
Really, just two options.
1. LeBron's philanthropy: While, he will continue to do things for UA, doubt it will ever be something like being the main donator/business partner for a new arena. I could see him chipping in some money to help an arena be financed (especially if there is a benefit to some of the things he does ... home for his skills academy and other basketball related ventures), but thinking he is gonna be the main force in a new arena is a pipedream.
2. Goodyear: this is the one multinational corporation, like B&G said, who could cut the check for their hometown. But while Goodyear is involved in sports, it is mainly automotive sports (NASCAR), which makes a ton of sense considering the business it is in. Still, the most likely, but would be a total philanthropic move. And since just keeping world headquarters, for better or worse reasons, is pretty philanthric in its own right. Doubt Goodyear believes it owes anymore to Akron than what it has been doing.
3. FirstMerit: this was the biggest dark horse since unlike Goodyear or FirstEnergy (Browns Stadium), it has no sports naming rights deals. But the Huntington deal killed that as Huntington was a big player in getting the new AAA stadium built in Columbus. It won't throw a bone to a regional hub like Akron. That's unfortunate because FirstMerit wasn't a distressed banking company that had to merge for survival.
Edit: I'll throw out one unmentioned new dark horse .... Key Bank. It's a top 20 banking company in the US and has some history of backing arenas (Key Center in Seattle). The Key Center was a 1960s venture (and I'm guessing Key wasn't interested in helping Seattle get a new arena since the Sonics moved to OKC.... Though it was a sham deal as the Sonics were moving to the owner's hometown regardless.) Anyway, with the loss of FirstMerit (and National City a few years back), maybe backing an arena in Akron could help strengthen its standing in NEO now that the two biggest competitors PNC/National City (Pittsburgh) and Huntington/FirstMerit (Columbus) are outsiders.