One of the first things people hear when they learn about using condoms is to remember that latex condoms (and therefore, latex dams and latex gloves) are not compatible with oil-based lubricants really, anything that contains oil at all.
Why is this? Oil of any kind is not good for latex. What it does is degrade the material, which significantly weakens it. While this is bad for latex in general (think hand lotion and a balloon), it is a huge issue regarding safer sex supplies.
Studies as far back as the late 80s and early 90s have shown that even small trace amounts of mineral oil (used in hand lotions, conditioners, and even some types of lubricants) can weaken a latex condom by 90%. The amount of exposure used in these studies was just sixty seconds.
If 90% of the strength of a condom can disappear with just one minute of exposure to oil, imagine how significantly weakened a condom could be during ten, fifteen, or even twenty minutes of exposure to oil-based lubricants.
It is important to remember that all oil types can challenge a latex condom's structural integrity, not just oil-based lubricants. This means that you want to stay away from using things like massage oil and then using latex in the same area, wash your hands in between with soap and warm water, and don't use it in the same area in which you'll be using the condom, gloves or dam.
The same goes for using lotion; it's fine to put on hand and body lotion after your sexual exploits, but do not begin your moisturizing routine right before you get ready to get it on.
The same goes for using things like cooking oil either for moisturizing or massage olive oil, almond oil, walnut oil, sesame oil, coconut oil, etc., all still contain the same oil enzymes that break down latex.
If, for some reason, you HAVE to use an oil-based lubricant (which is not recommended for internal use anyways; keep it away from vaginal and anal tissue), and you want to continue to practice safer sex, you have the option of using polyurethane condoms, or vinyl/nitrile gloves, or saran wrap as a dam.
While not the optimal option, it is a much safer choice than risking your safer sex device breaking down in the middle of the action because you mixed oil and latex.