The two types of lysosomes are Peroxisomes which is a vesicle containing oxidases and catalase. It's located by the smooth ER of the animal cell.The second type of lysosme is the Proteasome which is a tiny barrel-shaped structure that contain proteases.ysosomes are distributed among different types of eukaryotic cells  by their level of nutrients. Cells processing a high quantity of  larger nutrients will generally have m … ore lysosomes than other  cells.