The lakes that Scalloper1 (and I) are most familiar with allow you to fish both sides of the border provided that you do not go into the coves on the Canadian side. You can fish the main portion of the lake with either a Maine or New Brunswick license. The same is true on rivers along the international border between New Brunswick and Maine. I was checked 2 winters ago and was definitely over the line by US Border Patrol and Canadian authorities without any issue. In fact just this past winter, the Canadians were more interested in learning how to use a flasher and jig for togue. And yes, Trump was President.
It is not the case on boundary waters between Maine and Quebec and apparently between New York and Ontario..