  We have applied nuclear magnetic resonance spectroscopy to study the
distinctive network of nodal lines in the Dirac semimetal ZrSiTe. The low-$T$
behavior is dominated by a symmetry-protected nodal line, with NMR providing a
sensitive probe of the diamagnetic response of the associated carriers. A sharp
low-$T$ minimum in NMR shift and $(T_1T)^{-1}$ provides a quantitative measure
of the dispersionless, quasi-2D behavior of this nodal line. We also identify a
van Hove singularity closely connected to this nodal line, and an associated
$T$-induced Lifshitz transition. A disconnect in the NMR shift and line width
at this temperature indicates the change in electronic behavior associated with
this topological change. These features have an orientation-dependent behavior
indicating a field-dependent scaling of the associated band energies.
