Well, assuming it is one based on abuse of market power and not the other kinds of antitrust violations (e.g., combination in restraint of trade, etc.), it would fail if the plaintiff couldn't establish that Apple had market power in the market for the product for which they allegedly abused market power. If that was iPhones, for instance, that would be the market for iPhones plus whatever products empirically people substitute for iPhones in response to pricing changes. (Of course, if Apple has market power, there is some range in which the “plus...” part is “none”, since market or pricing power is the ability to raise prices without driving sales to a competing good.)
If the lawsuit was about selling some popular class of app in which Apple leveraged its monopoly over app distribution, I think the plaintiff could have a pretty strong case.
Keep in mind that even if Apple only had 1% market share in the smartphone market they would still have a "monopoly" over app distribution on their own phones.