The phenomenon of self-assembly of constituent elements to form molecules at low temperatures appears ubiquitously in transition metal compounds with orbital degrees of freedom. Recent progress in local structure studies using synchrotron radiation x-rays is shifting the interest in structural studies in such molecule-forming systems from the low-temperature ordered phase to the short-range order that appears like a precursor at high temperatures. In this study, we discuss both experimentally and theoretically the relationship between the trimer structure that appears in the layered LiV$X_2$ ($X$ = O, S, Se) system with a two-dimensional triangular lattice of vanadium and the zigzag chain-like local structure that appears near the phase transition boundary where molecular formation occurs. The vanadium trimerization that persistently appears in both low-temperature phases of LiVO$_2$ and LiVS$_2$ disappears in LiVSe$_2$, and a regular triangular lattice is thought to be realized in LiVSe$_2$, but this study reveals that the zigzag chain local distortion appears with a finite correlation length. This zigzag chain state local distortions are similar to the motif of local distortions in the high-temperature phase of LiVS$_2$, indicating that the local distortions are persistent away from the trimer phase transition boundary. On the other hand, it is concluded that the zigzag chain order appearing in LiVSe$_2$ is more stable than that in LiVS$_2$ in terms of the temperature variation of atomic displacement and correlation length. The zigzag chain order is considered to be competitive with the trimer order appearing in the LiV$X_2$ system. In this paper, we discuss the similarities and differences between the parameters that stabilize these electronic phases and the local distortions that appear in other molecular formation systems.
