The K-Best Solutions box on the Integer Solver tab:

is used to set the number of solutions desired as part of the K-Best solutions feature of LINGO's mixed integer solver.  Whenever this value is greater than 1, say K, LINGO will will return up to K unique solutions to the model.  These solutions will have the property that they are the next best solutions available in terms of their objective values.  Less than K solutions may be returned if a sufficient number of feasible solutions do not exist.  An example of the K-Best feature follows..