Now CL has a de facto monopoly, but it's like many others in that the market has granted that status to a large extent. CL can afford to look frumpy because it has few competitors and a massive first-mover advantage. You could set up 'Cushman's list' tomorrow and you'd probably crash and burn without them lifting a finger to obstruct you. So CL's listings are more than mere facts, they're the expression of a commercial preference by advertisers. A better comparison owuld be with stock exchange data; (as far as I know) the copyright on that is watertight because it's partly an expression of member companies' desire to be listed on that exchange as opposed to one of the competing exchanges.
The above is just my hunch about the copyright claim, but I don't think 3taps can succeed with that argument. The antitrust claim, I have no idea - but it should be borne in mind that monopolies are not necessarily bad. Courts nowadays give great weight to consumer benefit rather than abstract rules, and CL delivers an awful lot of consumer benefit by being free for most and charging very modest fees to a small class of advertisers.