In some people if the appendix is removed via surgery for various reasons what about the lymphatic mechanism that the appendix plays??

The appendix is a vestige of creation. In short, you do not need to have it. There are many people walking around without their appendices who have no problems. The appendix may have played a role in storage of colonic bacteria or digestion in our ancient ancestors. It is one of many areas in your intestine to have a high concentration of immune cells called GALT