Quadratic models must be convex in order for them to be solved by the quadratic solver.  You must disable the quadratic solver by turning off Quadratic Recognition and then re-solve.  You can disable Quadratic Recognition with the command:

 LINGO | Options | Nonlinear Solver | Quadratic Recognition

With command-line versions of LINGO, use the command:

 SET USEQPR 0

This will cause the general purpose, nonlinear solver to be invoked.  Please see the section titled Convexity for more information.