Hydrogels of amyloid fibrils are a versatile biomaterial for tissue engineering and other biomedical applications. Their suitability for these applications has been partly ascribed to their excellent and potentially engineerable rheological properties. However, while in biomedical applications the gels have to function in compositionally complex physiological solutions, their rheological behavior is typically only characterized in simple buffers. Here we show that the viscoelastic response of networks of amyloid fibrils of the protein lysozyme in biologically relevant solutions substantially differs from the response in simple buffers. We observe enhanced energy dissipation in both cell culture medium and synovial fluid. We attribute this energy dissipation to interactions of the amyloid fibrils with other molecules in these solutions and especially to the adsorption of the abundantly present protein serum albumin. This finding provides the basis for a better understanding of the performance of amyloid hydrogels in biomedical applications.