Deposits of insoluble protein plaques, which are mostly composed of fibrils from disease-specific amyloid proteins, are histological markers of various human disorders. These range from non-neuropathic amyloidosis such as light chain amyloidosis or type II diabetes to well-known neuro-degenerative diseases such as Alzheimer's Disease and Parkinson's Disease. There are indications that these types of fibrillar suprastructures display biological activity distinct from the individual fibrils they are composed of. Yet, little is known about the mechanisms underlying the assembly of fibrillar suprastructures. An understanding of secondary fibril self-assembly into mesoscopic and macroscopic suprastructures is also critical for their application as novel biomaterial. The paucity of experimental data and theoretical models on fibrillar supra-assembly likely relates to the experimental and conceptual challenges in following this type of assembly on multiple length- and timescales, and in characterizing the distinct morphologies formed. Here, we report that the amyloid dye thioflavin T (ThT) is augmented during self-assembly of isolated lysozyme fibrils. We provide evidence that this augmentation of ThT fluorescence results from the unquenching of fibril-bound ThT during fibril binding. Combining ThT fluorescence, optical density, and fluorescence quenching kinetics with optical and electron microscopy, we propose that fibril self-assembly is driven by a transition from reaction-limited ordered assembly to diffusion-limited random cross-linking of fibrils.