Nephi tells us that Lehi had "his own house at Jerusalem" (1 Nephi 1:7). He left that house and also "the land of his inheritance" (1 Nephi 2:4) which would have been outside the holy city, presumably in the lands of Manasseh north of Jerusalem, for Lehi was "a descendant of Manasseh" (Alma 10:3). Archaeologists have found the remains of free-standing houses in Jerusalem in Lehi’s day, so we at least have some idea of what his Jerusalem house might have looked like.
If he lived in a typical three-parallel room house, the rooms would have been only about ten feet wide. So, they were living in pretty cramped quarters. Even if they had a larger four-room house, Lehi and Sariah—along with all of their children (four sons and potentially a couple daughters), and probably some of their relatives—all lived in fairly close quarters, where privacy would have been scarce. Thus, Lehi had gone out onto a hillside somewhere to pray. But, as Jeff Chadwick has especially discussed, that was how domestic life was in those days.
Jeffrey R. Chadwick, "Lehi’s House at Jerusalem and the Land of His Inheritance," in Glimpses of Lehi’s Jerusalem, 81–130.