Question

Why the lysosomal membrane is not digested by lysosomal enzymes ?

Answer 1

Because its membrane contain  acidic enzymes called acid hydrolases.Abd these enzymes maintain the pH of lysosomes and can harm the cell if they eat its membrane

Answer 2

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Inside the lysosome membrane there is a thick "glycocalix" protective layer. This glycocalix is formed by lysosomal integral and peripheral membrane proteins, which are highly N-glycosylated with polylactosamine units and therefore highly resistant toward lysosomal digestion.