As far as I understand from your question, you want to separate LiBr from water. If you use solar energy, water will evaporate and LiBr salt will remain.
In a LiBr-H2O absorption system water is the refrigerant which is absorbed by the concentrated LiBr solution in the absorption unit before it is pumped into the generator where the solution is heated and again water vapor is released to the condensing unit. So you cannot get rid of the pump which is necessary for completing the cooling process and the energy needed to drive it is almost negligible.