Morphological features: Lysosomes are roughly spherical bodies enclosed by a single membrane. Peroxisomes are about the size of lysosomes and like them are enclosed by a single membrane.
functional similarity: 
Lysosomes and peroxisomes both break down substances within the cell. 
lysosomes break down materials ingested by the cell using hydrolytic enzymes at a pH of around 5. They also remove old cellular components and replace with newer ones. peroxisomes are responsible for the creation of hydrogen peroxide within a cell and are used to break down fats into usable molecules, as well as catalyze detoxification reactions in the liver.