  We prove a general theorem which allows the determination of Lie symmetries
of Laplace equation in a general Riemannian space using the conformal group of
the space. Algebraic computing is not necessary. We apply the theorem in the
study of the reduction of Laplace equation in certain classes of Riemannian
spaces which admit a gradient Killing vector, a gradient Homothetic vector and
a special Conformal Killing vector. In each reduction we identify the source of
Type II hidden symmetries. We find that in general the Type II hidden
symmetries of Laplace equation are directly related to the transition of the
CKVs from the space where the original equation is defined to the space where
the reduced equation resides. In particular we consider the reduction of
Laplace equation (i.e. the wave equation) in Minkowski space and obtain the
results of all previous studies in a straightforward manner. We consider the
reduction of Laplace equation in spaces which admit Lie point symmetries
generated from a non gradient HV and a proper CKV and we show that the
reduction with these vectors does not produce Type II hidden symmetries. We
apply the results to General Relativity and consider the reduction of Laplace
equation in locally rotational symmetric space times (LRS) and in algebraically
special vacuum solutions of Einstein's equations which admit a homothetic
algebra acting simply transitively. In each case we determine the Type II
hidden symmetries.
