  In this paper, we obtain an upper bound on the higher topological complexity
of the total spaces of fibrations. As an application, we improve the usual
dimensional upper bound on higher topological complexity of total spaces of
some sphere bundles. We show that this upper bound on the higher topological
complexity of the total spaces of fibrations can be improved using the notion
of higher subspace topological complexity. We also show that the usual
dimensional upper bound on the higher topological complexity of any
path-connected space can be improved in the presence of positive dimensional
compact Lie group action. We use these results to compute the exact value of
higher topological complexity of higher dimensional lens spaces in many cases.
