The present work proposes a novel method to achieve free phase propagation with unitary transmission efficiency, termed as lattice invisibility effects, based on transverse scattering in 1D cylindrical metalattices. Firstly, we extend Kerker conditions parity symmetry of electromagnetic modes, and a conciser scheme to eliminate both forward and backward scattering simultaneously is presented. Compared to sphere-like particles where the first four Mie modes are required, we find that transverse scattering can be realized here if only two resonances with similar parity symmetry have the same amplitude and opposite phase, because of reduced symmetry in cylindrical systems. Further, we generalize this concept to metalattices and propose an explicit principle to realize lattice transparency, as long as all the modes with similar parity profiles interfere destructively. The proof-of-concept demonstrations have been manifested by exciting pure degraded electric dipoles or co-exciting magnetic dipole and electric quadrupoles using SiO2@InSb or Si@InSb cylinders, respectively. Besides, the invisibility performance can be flexibly tuned by changing either the period of metalattices or the magnitude of external magnetic field. The revealed mechanisms will inspire more comprehensive study of directional scattering and free phase propagation, which can also potentially stimulate several advanced applications like optical cloaking, nanophotonic circuits, etc.