  We theoretically investigate defect formation energies in LaO$X$S$_2$
($X=$Sb, Bi) using first-principles calculation. We find that the oxygen
vacancy is relatively stable, where its formation energy is higher in $X=$ Sb
than in $X=$ Bi. An interesting feature of $X=$ Sb is that the vacancy of the
in-plane sulfur atom becomes more stable than in $X=$ Bi, caused by the
formation of an Sb$_2$ dimer and the electron occupation of the impurity energy
levels. The formation energies of cation defects and anion-cation antisite
defects are positive for the chemical equilibrium condition used in this study.
Fluorine likely replaces oxygen, and its defect formation energy is negative
for both $X=$ Sb and Bi, while that for $X=$ Sb is much higher than $X=$ Bi.
Our study clarifies the stability of several point defects and suggests that
the in-plane structural instability is enhanced in $X=$ Sb, which seems to
affect a structural change caused by some in-plane point defects.
