  We study the space-times of non-extremal intersecting p-brane configurations
in M-theory, where one of the components in the intersection is a ``NUT,'' i.e.
a configuration of the Taub-NUT type. Such a Taub-NUT configuration
corresponds, upon compactification to D=4, to a Gross-Perry-Sorkin (GPS)
monopole. We show that in the decoupling limit of the CFT/AdS correspondence,
the 4-dimensional transverse space of the NUT configuration in D=5 is foliated
by surfaces that are cyclic lens spaces S^3/Z_N, where N is the quantised
monopole charge. By contrast, in D=4 the 3-dimensional transverse space of the
GPS monopole is foliated by 2-spheres. This observation provides a
straightforward interpretation of the microscopics of a D=4 string-theory black
hole, with a GPS monopole as one of its constituents, in terms of the
corresponding D=5 black hole with no monopole. Using the fact that the
near-horizon region of the NUT solution is a lens space, we show that if the
effect of the Kaluza-Klein massive modes is neglected, p-brane configurations
can be obtained from flat space-time by means of a sequence of dimensional
reductions and oxidations, and U-duality transformations.
