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.