  In this paper, we study the problem of gathering distance-1 myopic robots on
an infinite triangular grid. We show that the algorithm developed by Goswami et
al. (SSS, 2022) is lattice-linear (cf. Gupta and Kulkarni, SRDS 2023). This
implies that a distributed scheduler, assumed therein, is not required for this
algorithm: it runs correctly in asynchrony. It also implies that the algorithm
works correctly even if the robots are equipped with a unidirectional
\textit{camera} to see the neighbouring robots (rather than an omnidirectional
one, which would be required under a distributed scheduler). Due to
lattice-linearity, we can predetermine the point of gathering. We also show
that this algorithm converges in $2n$ rounds, which is lower than the
complexity ($2.5(n+1)$ rounds) that was shown in Goswami et al.
