Lobbying in the EU is far less difficult than you seem to be implying, and US corporations especially enjoy their access to policymakers in the EU, perhaps because of its bureaucratic nature with a degree of separation between popular political contests, which  frequently throws wrenches into things in the US.

The classic academic paper demonstrating how corporations easily take over policymaking in the EU, even when other groups such as NGO's are provided explicit institutional access alongside such corporations, is "Leading the Dance: Power and Political Resources of Business Lobbyists," by Cornelia Woll (2007).

In the last US election, the corporate class all backed Clinton, overwhelmingly, financially and otherwise, outspending Trump by an order of magnitude. Trump may be friendly to some kinds of business in some ways, but is mostly an unwelcome wildcard as far as the vast majority of billionaire class's lobbyists are concerned.

Looked at through economic theory, trade policies which lead to large, regulatory-homogenized markets is in the best interests of large corporations because it increases the returns to scale, an implication of the work by economics Nobel laureate Paul Krugman. That has been the global policy trajectory for decades under US global leadership. Now that train has been thrown off the tracks by Trump.