  We, firstly, improve a theorem of B. Roberts which characterizes
non-vanishing of a global theta lift from O(X) to Sp(n) in terms of
non-vanishing of local theta lifts. In particular, we will remove all the
archimedean conditions imposed upon his theorem. Secondly, following Roberts,
we will apply our theorem to theta lifting of low rank similitude groups.
Namely we characterize the non-vanishing condition of a global theta lift from
GO(4) to GSp(2) in our improved setting. Also we consider non-vanishing
conditions of a global theta lift from GO(4) to GSp(1) and explicitly compute
the lift when it exists.
