Hen egg white lysozyme was employed for studying aggregation and nucleation events induced by simple electrolytes such as NaCl while the process was monitored by time-resolved, small-angle static light scattering. The fractal dimension, the weight-average molecular weight, the mean radius of gyration and the homogeneity exponent, which typify cluster reactivity, were determined as a function of the elapse reaction time. The observed clusters resemble mass-fractals; however, direct classification to the limiting diffusion or reaction aggregation regimes is not straightforward and the findings verify deviations postulated in previous works. In nucleating solutions the interplay between packing and electrostatics makes the situation more complex than anticipated so far. A delicate balance exists between the conditions that optimize charge screening and those promoting gel formation. A nonmonotonic behavior of dimensionalities and exponents is observed when the latter are plotted as a function of lysozyme or electrolyte concentration. The implications of fractal structure formation during the nucleation of lysozyme are discussed.