  The TeV binary system \lsi has a compact object in an eccentric orbit around
a Be star about 2 kpc from Earth. \lsi exhibits modulated gamma-ray emission
around its 26.5 days orbit, mostly detectable at TeV energies around its
apastron passage, with maximum flux during the $\phi = 0.55-0.65$ phase range.
Multiple flaring episodes with nightly flux variability at TeV energies have
been observed since its detection in 2006. At one time significant TeV emission
was also detected in late 2010 from the source close to its periastron passage
at superior conjunction. The TeV spectrum is well fitted by a power law with
small variations of spectral index of $\sim2.6$ over the years. GeV, X-ray, and
radio emission have been detected along the entire orbit, enabling detailed
study of the modulation pattern and its super-orbital period, such
comprehensive study of the \lsi orbit in the TeV regime has not been presented
before. VERITAS has observed \lsi for over a decade now, accruing 200+ hours of
data during different parts of its orbit. In this work, we have analyzed all
available data for \lsi since September 2007 in individual phase bins of width
$\Delta \phi = 0.1$ and performed a spectral analysis for two different parts
of the orbit. TeV emission is now detected in 9 out of 10 phase bins, around
the entire orbit for the first time in VERITAS data. Hint of spectral variation
might also be present between different parts of the orbit. The implication of
these results is discussed in the context of determining the nature of the
unknown compact object (neutron star or microquasar) and a discussion of the
absorption mechanisms in the system.
