The wax and oil content in most lipsticks is what makes it difficult to remove from fabrics, crockery and your HuskeeCups.
Try applying a small amount of dishwashing detergent straight on the stain and rubbing with a damp micro-fibre cloth. If the stain persists, soak HuskeeCups in a tub of hot water with 1 tsp of espresso machine cleaner per cup, for 8 hours/overnight. This should lift most stains from your HuskeeCup
DO NOT use abrasive cleaners such as a scourer as this will permanently damage your cups.