The boundary waters, the border waters, the border lakes, the Canadian waters, the canoe country, the wilderness waters, and the north country, all are used to refer to the lakes laying along the Minnesota / Ontario International Border. Generically, if talking about the entire area, any of these would be correct.
There are, however, actually two governments involved, and two totally separate areas: The Boundary Waters Canoe Area Wilderness on the United States side, and Quetico Provincial Park on the Canadian side. Normally, the US side is referred to the BWCA, and the Canadian side is referred to as Quetico (QWIH-tih-co).
Oh, and by the way, the little Minnesota town laying in the middle of the southern edge of the BWCA is pronounced E-lee as in REALLY (not E-lie, nor EL-lee).