  We present a study on the detailed elemental abundances of newly identified
bright very metal-poor stars with the detection of lithium, initially observed
as part of the SDSS/MARVELS pre-survey. These stars were selected for
high-resolution spectroscopic follow-up as part of the HESP-GOMPA survey. In
this work, we discuss the Li abundances detected for several stars in the
survey, which include main-sequence stars, subgiants, and red giants. Different
classes of stars are found to exhibit very similar distributions of Li, which
point towards a common origin. We derive a scaling relation for the depletion
of Li as a function of temperature for giants and main-sequence stars; the
majority of the samples from the literature were found to fall within 1sigma
(0.19 and 0.12 dex/K for giants and dwarfs respectively) of this relationship.
We also report the existence of a slope of the Li abundances as a function of
distances from the Galactic plane, indicating mixed stellar populations. Most
Li-rich stars are found to be in or close to the galactic plane. Along with Li,
we have derived detailed abundances for C, odd-Z, alpha-, Fe-peak, and
neutron-capture elements for each star. We have also used astrometric
parameters from Gaia-EDR3 to complement our study, and derived kinematics to
differentiate between the motions of the stars; those formed in situ and
accreted. The stellar population of the Spite plateau, including additional
stars from the literature, is found to have significant contributions from
stars formed in situ and through accretion. The orbits for the program stars
have also been derived and studied for a period of 5 Gyr backward in time.
