  We present a high-significance cross-correlation of CMB lensing maps from the
Atacama Cosmology Telescope (ACT) Data Release 6 (DR6) with spectroscopically
calibrated luminous red galaxies (LRGs) from the Dark Energy Spectroscopic
Instrument (DESI). We detect this cross-correlation at a significance of
38$\sigma$; combining our measurement with the Planck Public Release 4 (PR4)
lensing map, we detect the cross-correlation at 50$\sigma$. Fitting this
jointly with the galaxy auto-correlation power spectrum to break the galaxy
bias degeneracy with $\sigma_8$, we perform a tomographic analysis in four LRG
redshift bins spanning $0.4 \le z \le 1.0$ to constrain the amplitude of matter
density fluctuations through the parameter combination $S_8^\times = \sigma_8
\left(\Omega_m / 0.3\right)^{0.4}$. Prior to unblinding, we confirm with
extragalactic simulations that foreground biases are negligible and carry out a
comprehensive suite of null and consistency tests. Using a hybrid effective
field theory (HEFT) model that allows scales as small as $k_{\rm max}=0.6$
$h/{\rm Mpc}$, we obtain a 3.3% constraint on $S_8^\times = \sigma_8
\left(\Omega_m / 0.3\right)^{0.4} = 0.792^{+0.024}_{-0.028}$ from ACT data, as
well as constraints on $S_8^\times(z)$ that probe structure formation over
cosmic time. Our result is consistent with the early-universe extrapolation
from primary CMB anisotropies measured by Planck PR4 within 1.2$\sigma$.
Jointly fitting ACT and Planck lensing cross-correlations we obtain a 2.7%
constraint of $S_8^\times = 0.776^{+0.019}_{-0.021}$, which is consistent with
the Planck early-universe extrapolation within 2.1$\sigma$, with the lowest
redshift bin showing the largest difference in mean. The latter may motivate
further CMB lensing tomography analyses at $z<0.6$ to assess the impact of
potential systematics or the consistency of the $\Lambda$CDM model over cosmic
time.
