The Aragorn and Arwen material in Return of the King Appendix A tells that after the death of Aragorn:
...Arwen went forth from the House, and the light of her eyes was quenched, and it seemed to her people that she had become cold and grey as nightfall in winter that comes without a star. Then she said farewell to Eldarion, and to her daughters, and to all whom she had loved; and she went out from the city of Minas Tirith and passed away to the land of Lórien, and dwelt there alone under the fading trees until winter came. Galadriel had passed away and Celeborn also was gone, and the land was silent.
There at last when the mallorn-leaves were falling, but spring had not yet come, she laid herself to rest upon Cerin Amroth; and there is her green grave, until the world is changed, and all the days of her life are utterly forgotten by men that come after, and elanor and niphredil bloom no more east of the Sea.
In other words Arwen, being heartbroken, leaves Gondor and goes to live in Lórien for a year or so before she died, and her grave just happened to be in the place she died in.