Protein-based nanocarriers are versatile and biocompatible drug delivery systems. They are of particular interest in nanomedicine as they can recruit multiple functions in a single modular polypeptide. Many cell-targeting peptides or protein domains can promote cell uptake when included in these nanoparticles through receptor-mediated endocytosis. In that way, targeting drugs to specific cell receptors allows a selective intracellular delivery process, avoiding potential side effects of the payload. However, once internalized, the endo-lysosomal route taken by the engulfed material usually results in full degradation, preventing their adequate subcellular localization, bioavailability and subsequent therapeutic effect. Thus, entrapment into endo-lysosomes is a main bottleneck in the efficacy of protein-drug nanomedicines. Promoting endosomal escape and preventing lysosomal degradation would make this therapeutic approach clinically plausible. In this review, we discuss the mechanisms intended to evade lysosomal degradation of proteins, with the most relevant examples and associated strategies, and the methods available to measure that effect. In addition, based on the increasing catalogue of peptide domains tailored to face this challenge as components of protein nanocarriers, we emphasize how their particular mechanisms of action can potentially alter the functionality of accompanying protein materials, especially in terms of targeting and specificity in the delivery process.