  In this work, we have assumed the generalized Vaidya solution in Lovelock
theory of gravity in $(n+2)$-dimensions. It has been shown that Gauss-Bonnet
gravity, dimensionally continued Lovelock gravity and pure Lovelock gravity can
be constructed by suitable choice of parameters. We have investigated the
occurrence of singularities formed by the gravitational collapse in above three
particular forms of Lovelock theory of gravity. The dependence of the nature of
singularity on the existence of radial null geodesic for Vaidya space-time has
been specially considered. In all the three models, we have shown that the
nature of singularities (naked singularity or black hole) completely depend on
the parameters. Choices of various parameters are shown in tabular form. In
Gauss-Bonnet gravity theory, it can be concluded that the possibility of naked
singularity increases with increase in dimensions. In dimensionally continued
Lovelock gravity, the naked singularity is possible for odd dimensions for
several values of parameters. In pure Lovelock gravity, only black hole forms
due to the gravitational collapse for any values of parameters. It has been
shown that when accretion is taking place on a collapsing object, it is highly
unlikely to get a black hole. Finally on considering the phantom era in the
expanding universe it is observed that there is no possibility of formation of
a black hole if we are in the Gauss-Bonnet gravity considering the accreting
procedure upon a collapsing object.
