In the following papers you find good descriptions of the lipid composition you can use to do a proper mimicking of the biological membrane:
Erazo-Oliveras, A., Najjar, K., Truong, D., Wang, T. Y., Brock, D. J., Prater, A. R., & Pellois, J. P. (2016). The late endosome and its lipid BMP act as gateways for efficient cytosolic access of the delivery agent dfTAT and its macromolecular cargos. Cell chemical biology, 23(5), 598-607.
Yang, S. T., Zaitseva, E., Chernomordik, L. V., & Melikov, K. (2010). Cell-penetrating peptide induces leaky fusion of liposomes containing late endosome-specific anionic lipid. Biophysical journal, 99(8), 2525-2533.
Jones, C. H., Chen, C. K., Ravikrishnan, A., Rane, S., & Pfeifer, B. A. (2013). Overcoming nonviral gene delivery barriers: perspective and future. Molecular pharmaceutics, 10(11), 4082-4098.
Chiplunkar, S. S., Silva, C. A., Bermudez, L. E., & Danelishvili, L. (2019). Characterization of membrane vesicles released by Mycobacterium avium in response to environment mimicking the macrophage phagosome. Future microbiology, 14(4), 293-313.
These two papers will help you related to your question.