This is debated among cell biologists, some say they do and others say they don't contain lysosomes. However, the general consensus I believe is that they do contain lysosomes because they have to have their degradative enzymes compartmentalized in this lysosome structure. Those that say they do not have lysosomes say that their enzymes are contained in just generalized vacuoles which are not lysosomes. But, most biologists say that these vacuoles are the equivalent to animal lysosomes.
So, yes both animals and plants contain lysosomes. I do know, however; that plants do not have centrosomes.