Multinational cooperations may be capitalistic, but aren't looked upon all that favorably in classical liberalism. Have you read Adam's Smith's Wealth of Nations? I admit I only read the first third or fourth of it and that was a couple years ago (it is a very boring and redundant text, with too many very old examples, but it does address a lot more issues than people give it credit for, even those related to game theory and environmentalism that we tend to think of of as being recent), but he was certainly not a fan of big business. The popular view of libertarianism may be one that favors big business and the rich, but that is not the case. Real libertarian ideas have never been given much of a chance to be tested, since people tend to favor it except when they think they personally would benefit from governmental interference. This often leads to corrupt, crony capitalism. In Erebus, that would be the economic model of choice for the Council of Esus and especially the Stewards of Inequity (these aren't in the game, but is the religion of those who worship Mammon--even though most of them don't realize they are doing so). It may be common in many empires, but this is a sign of the influence of Mammon. The good and neutral gods are very much opposed to it.
I'm not quite sure how FoL economies would work. It doesn't really have a unified dogma and its practices vary greatly, so the economies might too. I'd expect the good FoL civs to be similar to the Empyrean's libertarian type views, except emphasizing respect for all life instead of just sentient forms. For the Neutral ones they would take the last part a little too far, giving a forest much more respect than an individual human and probably creating a tightly controlled economy that protects trees more than people. I tend to think evil FoL civs follow extreme versions of Social Darwinism.