Lake Winnibigoshish Land Exchange Act of 2024 This bill directs the Forest Service to exchange specified land in the Chippewa National Forest in Minnesota for specified land owned by Big Winnie Land and Timber, LLC (BWLT), if BWLT offers to make the exchange. The land acquired by the Forest Service must be added to and managed as part of Chippewa National Forest. The bill outlines requirements and conditions for the exchange. For example, the Forest Service must reserve an easement for road access to certain land in the forest. The bill also conditions the exchange on the satisfactory completion of a Phase I Environmental Site Assessment by BWLT before the nonfederal land is accepted in the exchange. In addition, the exchange must be for equal value or the values must be equalized by a cash payment, subject to an exception. Finally, the bill directs BWLT to pay all closing costs associated with the exchange.