Right-handed lepton flavor mixing in the left-right symmetric model directly affects the production and decay of heavy Majorana neutrinos $N_R$, yet its impact on collider searches remains less explored. Using a deep neural network (DNN), we analyze the Keung-Senjanovi\'c process $pp \to W_R \to \ell_\alpha N_R \to \ell_\alpha \ell_\beta jj$ with $\ell_{\alpha,\beta}=e,\mu$ at LHC Run~2 and the HL-LHC, considering both same-sign and opposite-sign dilepton channels. We adopt three benchmark mixing scenarios: unmixed, maximal-mixing, and PMNS-like. In the unmixed scenario, the DNN improves the expected significance over the cut-based analyses performed by ATLAS, leading to stronger exclusion limits. For the combined $\ell\ell$ analysis, the HL-LHC can exclude $m_{W_R}$ and $m_{N_R}$ up to $6.7$ ($6.3$)~TeV and $4.4$ ($4.1$)~TeV, respectively, under maximal (PMNS-like) mixing. LHC Run~2 already excludes a significant portion of the $|V_{e1}|\text{--}|V_{\mu1}|$ plane, and the HL-LHC will probe even smaller mixing values, possibly ruling out both the maximal and PMNS-like patterns. Finally, we investigate complementarities with low-energy charged lepton flavor violation processes, where future searches can overlap with or exceed the LHC reach.