The formation of protein aggregates is important in many fields of life science and technology. The morphological and mechanical properties of protein solutions depend upon the molecular conformation and thermodynamic and environmental conditions. Non-native or unfolded proteins may be kinetically trapped into irreversible aggregates and undergo precipitation or gelation. Here, we study the thermal aggregation of lysozyme in neutral solutions. We characterise the irreversible unfolding of lysozyme by differential scanning calorimetry. The structural properties of aggregates and their mechanisms of formation with the eventual gelation are studied at high temperature by spectroscopic, rheological and scattering techniques. The experiments show that irreversible micron-sized aggregates are organised into larger clusters according to a classical mechanism of diffusion and coagulation, which leads to a percolative transition at high concentrations. At a smaller length scale, optical and atomic force microscopy images reveal the existence of compact aggregates, which are the origin of the aggregation irreversibility.