Like the guys have already said, it's not an either-or situation. It's entirely possible, and actually preferred, to be lifting if the goal is to drop fat. People that try losing "weight" without lifting (just using cardio and diet) may end up weighing less, but also end up soft, flabby, and weak.
If you guys will be training together during this friendly competition, even better. Pick out a decent program from the site, follow the plan, and push each other every session (without encouraging anything totally stupid, too often, at least).
EDIT - This: "Should You Really Get Lean Before Getting Big"
is a different situation than this: "Say your body fat percentage is between 17 and 23% and you want to get it down below 15%."
Lifting is a huge part of the plan, regardless. But if you're 20% and want to get down to 15%, the overall approach and the details will be different than if you're 20%, 180 pounds, and want to end up at 200 pounds.
To answer the thread title, yes, it's generally not recommended to try getting big/bulking up when you're already carrying a large amount of bodyfat. Has to do with insulin sensitivity, metabolic efficiency, and some other factors. But it's more about being "not fat", not necessarily getting "really lean."