  In this work a theorical framework to apply the Poincar\'e compactification
technique to locally Lipschitz continuous vector fields is developed. It is
proved that these vectors fields are compactifiable in the n-dimensional
sphere, though the compactified vector field can be identically null in the
equator. Moreover, for a fixed projection to the hemisphere, all the
compactifications of a vector field, which are not identically null on the
equator are equivalent. Also, the conditions determining the invariance of the
equator for the compactified vector field are obtained. Up to the knowledge of
the authors, this is the first time that the Poincar\'e compactification of
locally Lipschitz continuous vector fields is studied. These results are
illustrated applying them to some families of vector fields, like polynomial
vector fields, vector fields defined as a sum of homogeneous functions and
vector fields defined by piecewise linear functions.

Dynamical Systems