The performance of lysozyme adsorption by the aminated nanofiber membrane immobilized with Reactive Green 19 (RG19) dyes was evaluated in batch and flow systems. The physicochemical properties of the dye-immobilized nanofiber membrane were characterized. The parameters of batch-mode adsorption of lysozyme (e.g., pH, initial dye concentration, and lysozyme concentration) were optimized using the Taguchi method. In a flow process, the factors influencing the dynamic binding performance for lysozyme adsorption in the chicken egg white (CEW) solution include immobilized dye concentration, adsorption pH value, feed flow rate, and feed CEW concentration. The impact of these operating conditions on the lysozyme purification process was investigated. Under optimal conditions, the recovery yield and purification factor of lysozyme achieved from the one-step adsorption process were 98.52% and 143 folds, respectively. The dye-affinity nanofiber membrane also did not exhibit any significant loss in its binding capacity and purification performance after five consecutive uses.