We study the Lehmer sequences modulo $m$. Moreover, we define the Lehmer orbit and the basic Lehmer orbit of a
2-generator group $G$ for a generating pair $(x, y) \in G$ and examine the lengths of the periods of these orbits. Furthermore, we obtain the Lehmer lengths and the basic Lehmer lengths of the Fox groups $G_{1,t}$ for $t \geq 3$.
