  Lensing reconstruction maps from the cosmic microwave background (CMB)
provide direct observations of the matter distribution of the universe without
the use of a biased tracer. Such maps, however, constitute projected
observables along the line of sight that are dominated by their low-redshift
contributions. To cleanly access high-redshift information, Maniyar et al.
showed that a linear combination of lensing maps from both CMB and line
intensity mapping (LIM) observations can exactly null the low-redshift
contribution to CMB lensing convergence. In this paper we explore the
scientific returns of this nulling technique. We show that LIM-nulling
estimators can place constraints on standard $\Lambda$CDM plus neutrino mass
parameters that are competitive with traditional CMB lensing. Additionally, we
demonstrate that as a clean probe of the high-redshift universe, LIM-nulling
can be used for model-independent tests of cosmology beyond $\Lambda$CDM and as
a probe of the high-redshift matter power spectrum.
