One of the essential requirements for any camp that would be used for longer than a day is access to water. Thus, the first camp occurs near a river. It has been assumed that this must be a river that flowed all year round. That requirement is difficult to fill in that region, although there is a good candidate in the Wadi Tayyib al-Ism. However, it may not actually be a requirement for the physical location.
Hugh Nibley noted that Lehi is using what has been a recorded from Bedouin poetry. It is inspired by the site of running water, is addressed to one or two traveling companions (who are admonished to be like the thing beheld) and is typically quite short, consisting of two couplets.
The literary function of this prayer, or blessing, is to encourage Laman and Lemuel to become something that they are not yet. Certainly, the steadfast valley supports that imagery. What then of the continually running river? Since Lehi probably could not have known if it was a year-round river, the imagery is apt for any river. All rivers run continuously—until they have no water. While there is water, the river is defined by that water running.
If Lehi is intent on this poetic form and its lessons for his sons, the continually running water is the metaphor extracted from the current scene, and not necessarily a physical qualification of the river he saw.
For Nephi, who is including this poem, the function is to begin to paint the picture of how Lehi’s two eldest sons eventually become the sworn enemies of those who follow Nephi. It is the poem, not the geography, that is important.