  In 2010, M. Sakai and the first author showed that the topological complexity
of a space $X$ coincides with the fibrewise unpointed L-S category of a pointed
fibrewise space $\operatorname{pr}_{1} : X \times X \to X$ with the diagonal
map $\Delta : X \to X \times X$ as its section. In this paper, we describe our
algorithm how to determine the fibrewise L-S category or the Topological
Complexity of a topological spherical space form. Especially, for $S^3/Q_8$
where $Q_8$ is the quaternion group, we write a python code to realise the
algorithm to determine its Topological Complexity.
