  LaTe$_3$ is a noncentrosymmetric (NC) material with time reversal (TR)
symmetry in which the charge density wave (CDW) is hosted by the Te bilayers.
Here, we show that LaTe$_3$ hosts a Kramers nodal line (KNL), a twofold
degenerate nodal line that connects the TR invariant momenta in NC achiral
systems, using angle resolved photoemission spectroscopy (ARPES), density
functional theory (DFT), effective band structure (EBS) calculated by band
unfolding, and symmetry arguments. DFT incorporating spin-orbit coupling (SOC)
reveals that the KNL -- protected by the TR and lattice symmetries -- imposes
gapless crossings between the bilayer-split CDW-induced shadow bands and the
main bands. In excellent agreement with the EBS, ARPES data corroborate the
presence of the KNL and show that the crossings traverse the Fermi level.
Furthermore, spinless nodal lines - entirely gapped out by the SOC - are formed
by the linear crossings of the shadow and main bands with a high Fermi
velocity.
