  Using {\it ab initio} density functional theory, we study the lattice phase
transition of quasi-one-dimensional (TaSe$_4$)$_2$I. In the undistorted state,
the strongly anisotropic semimetal band structure presents two non-equivalent
Weyl points. In previous efforts, two possible Ta-tetramerization patterns were
proposed to be associated with the low-temperature structure. Our phonon
calculations indicate that the orthorhombic $F222$ CDW-I phase is the most
likely ground state for this quasi-one-dimensional system. In addition, the
monoclinic $C2$ CDW-II phase may also be stable according to the phonon
dispersion spectrum. Since these two phases have very similar energies in our
DFT calculations, both these Ta-tetramerization distortions likely compete or
coexist at low temperatures. The semimetal to insulator transition is induced
by a Fermi-surface-driven instability that supports the Peierls scenario, which
affects the Weyl physics developed above $T_{\rm CDW}$. Furthermore, the
spin-orbit coupling generates Rashba-like band splittings in the insulating CDW
phases.
