Aims. We use the angular cross-correlation between a luminous red galaxy (LRG) sample from the Dark Energy Spectroscopic Instrument (DESI) Legacy Survey data release DR9 and the Planck cosmic microwave background (CMB) lensing maps to constrain the local primordial non-Gaussianity parameter, fNL, using the scale-dependent galaxy bias effect. The galaxy sample covers approximately 40% of the sky, contains galaxies up to redshift z ∼ 1.4, and is calibrated with the LRG spectra that have been observed for DESI Year 1 (Y1). Methods. We apply a nonlinear imaging systematics treatment based on neural networks to remove observational effects that could potentially bias the fNL measurement. Our measurement is performed without blinding, but the full analysis pipeline is tested with simulations including systematics. Results. Using the two-point angular cross-correlation between LRG and CMB lensing only, we find fNL = 39‑38+40 at the 68% confidence level, and our result is robust in terms of systematics and cosmological assumptions. If we combine this information with the autocorrelation of LRG, applying a scale cut to limit the impact of systematics, we find fNL = 24‑21+20 at the 68% confidence level. Our results motivate the use of CMB lensing cross-correlations to measure fNL with future datasets, given its stability in terms of observational systematics compared to the angular autocorrelation. Furthermore, performing accurate systematics mitigation is crucially important in order to achieve competitive constraints on fNL from CMB lensing cross-correlation in combination with the tracers' autocorrelation.