Note that the place is not necessarily well known as "Shazer", but that "we did call the name of the place Shazer." Nibley notes:
"Then it says they took their journey in "nearly a south-southeast direction [from that time forth] and we did pitch our tents again; and we did call the name of the place Shazer.". . . Shazer is a clump of trees . . . It's a group of trees in the desert. Well, naturally, the place they would park next would be where there were some trees, some water, etc. So they camped in a place call Shazer, "the trees"( Hugh Nibley, Teachings of the Book of Mormon, Semester 1, p.216-17).
Reynolds and Sjodahl give a different possibility for the name "Shazer. This name may have been, originally, the Hebrew chazer (or chazier), "grass" (Ps. 104:14) (Reynolds and Sjodahl, Commentary on the Book of Mormon, Vol. 1., p.166).
It took them four days to arrive at this location. It is not known precisely how far they were able to travel in a day's time. John Sorenson has done some research on the distances that various peoples might travel in a day:
"Mormon pioneers driving ox teams across flat Nebraska averaged 10 to 11 miles a day. In Guatemala it takes drovers eight days to herd pigs 90 miles through mountainous terrain to market - an average of little more than 11 miles a day. Other groups of travelers don't move even this fast. R. E. W. Adams, an archaeologist who has worked in Guatemala, reports that travelers on the routine trading trips on jungle trails and streams from the Cotzal Valley of the Peten, about 120 air miles away, take 19 days or more, averaging a little more than six miles a day. Much of their trip is via dugout canoe down rivers. Furthermore, a person walking in that area can cover in six hours a distance that would take seven riding a horse. If he drives animals along, the time stretches out to ten hours.
Other travelers are much speedier. R.F. Heizer reports that in the nineteenth century small groups of Mohave Indians in California could cover nearly 100 miles a day, sometimes going without food or even water for days." (John Sorenson, _An Ancient American Setting for the Book of Mormon_, FARMS, 1985, pp.8-9).
Based on estimates of travel, we might assume that the party traveled perhaps up to 25 miles per day, making the distance from Lemuel to Shazer between 60-100 miles. One suggestion for a possible location of Shazer has been Al Azlan (Allen, Exploring the Lands of the Book of Mormon, p. 264).