No, while Lull mattresses may have removable covers, they should never be cleaned in a washer or dryer. Doing so may cause it to shrink or even be damaged, which would not be covered by the warranty.
To clean specific spots or stains, Lull recommends using a cleaning solution of a 1-to-3 ratio of dish soap to water. They stress not getting the mattress too wet and to allow it to air-dry before putting bedding back on. For heavier stains, you could also try baking soda, hydrogen peroxide, and a drop or two of dish soap.
If you want a cover that is fully machine washable, Lull sells a separate mattress protector that will be your best bet.
