  The current claim by Grebenev et al. [J. Phys. A: Math. Theor. 52, 335501
(2019)], namely that the inviscid and unclosed 2D Lundgren-Monin-Novikov (LMN)
equations on a zero-vorticity Lagrangian path admit conformal invariance, is
based on a flawed and misleading analysis published earlier by Grebenev et al.
(2017). All false results and conclusions made before in the Eulerian picture
were now extended by Grebenev et al. (2019) to the Lagrangian picture. Although
we have already commented on these errors and consistently refuted their
previous study (Frewer & Khujadze, 2018), we deem it necessary to address and
discuss these errors again in the new formulation and notation of Grebenev et
al. (2019) as it will offer new insights into this issue.
