Answer:
We do not really know…as far as the history of Lot it ends with this…
Genesis 19:30-38 And Lot went up out of Zoar, and dwelt in the mountain, and his two daughters with him; for he feared to dwell in Zoar: and he dwelt in a cave, he and his two daughters. And the firstborn said unto the younger, Our father is old, and there is not a man on the earth to come in unto us after the manner of all the earth: Come, let us make our father drink wine, and we will lie with him, that we may preserve descendants of our father. And they made their father drink wine that night: and the firstborn went in, and lay with her father; and he knew not when she lay down, nor when she arose. And it came to pass on the next day, that the firstborn said unto the younger, Behold, I lay last night with my father: let us make him drink wine this night also; and you go in, and lie with him, that we may preserve descendants of our father. And they made their father drink wine that night also: and the younger arose, and lay with him; and he knew not when she lay down, nor when she arose. Thus were both the daughters of Lot with child by their father. And the firstborn bore a son, and called his name Moab: the same is the father of the Moabites unto this day. And the younger, she also bore a son, and called his name Benammi: the same is the father of the children of Ammon unto this day.
There are other places in the Bible it talks about Lot after this point, but not to tell us anything more specifically about his death or burial place.