The 1841 British edition omitted the preposition with from this clause. The expression “to camp one’s army” seems problematic. It is not surprising that the subsequent LDS edition (in 1849) restored the with. Moreover, the preceding text provides additional support for the preposition with: “to spy out in what part of the city the Lamanites did camp with their army” (Alma 62:20). In any event, the earliest text for Alma 62:22 has the with, and the critical text will follow that reading.
Summary: Maintain in Alma 62:22 the preposition with in “where the Lamanites did not camp with their armies”.