We examine the constraints coming from the leptonic sector on the parameter space of the alternative left-right model. We focus on flavour-conserving observables, the muon anomalous magnetic moment, and flavour-violating processes, \(\mu \rightarrow e\gamma \)  decay and \(\mu \rightarrow e\) conversion in \(\textrm{Al}\) nuclei. We perform the multidimensional scans of the model parameter space and show that the contributions to the anomalous magnetic moment remain below the experimental measured value at \(2\sigma \) . In addition, the current and future experimental sensitivities to flavour-violating muon processes are expected to put stringent lower bounds on the masses of the exotic gauge bosons of the model.