  Intermediate redshifts between galaxy surveys and the cosmic microwave
background (CMB) remain unexplored territory. Line intensity mapping (LIM)
offers a way to probe the $z\gtrsim 1$ Universe, including the epoch of
reionization and the dark ages. Via exact nulling of the lensing kernel, we
show that LIM lensing, in combination with galaxy (resp., CMB) lensing, can
uniquely probe the $z\gtrsim 1$ (resp., pre-reionization) Universe. However,
LIM foregrounds are a key hurdle to this futuristic technique. While continuum
foregrounds can be controlled by discarding modes perpendicular to the line of
sight (low $k_\parallel$ modes), interloper foregrounds haven't been addressed
in the context of LIM lensing. In this paper, we quantify the interloper bias
to LIM lensing for the first time, and derive a ''LIM-pair'' estimator which
avoids it exactly after cross-correlating with CMB lensing. This new quadratic
lensing estimator works by combining two intensity maps in different lines,
from the same redshift, whose interlopers are uncorrelated. As a result, this
foreground avoidance method is robust to even large changes in the amplitude of
the interloper power and non-Gaussianity. The cross-spectrum of the LIM-pair
estimator with CMB lensing is thus robust to the currently large theoretical
uncertainties in LIM modeling at high redshift.
