Although it is a popular myth that mayonnaise makes for a good personal lubricant, the truth is that it is not nearly as effective as the more mainstream options. Those who are desperate and cannot find anything else to use when they need a lubricant might want to give mayonnaise a try, simply because it contains so many oils and is in fact partially liquid and partially a solid.
While it may not be as effective as most commercial lubricants which are specifically designed for this purpose, in theory mayonnaise could work depending on what you are using it for.