Half the job of a map maker is to figure out correct borders in disputed areas while keeping both sides happy. In the internet age they can do that by simply showing a different map in each country.

What's the purpose of a map if not to reflect how people actually refer to and interact with these features? Disputed borders are handled that way because people inside those countries have understandings of "their" borders (and it's politically convenient for the companies involved). The term "Lake America" isn't in active use as a geographic referrant, so there's no point reflecting it in a map beyond the political convenience.