It is best to make time. Even a 30 min walk 3 times a week is better than nothing because even if you manage your diet well, the body will lose muscle over time and it is much easier to maintain a lean body with the proper exercise and diet.
With that being said, you can lose weight without exercise by managing your diet. Find out how many calories you burn in a day and then plan a diet based on 500 less calories. Try and eat 5 times a day to keep your metabolism as high as it can get. Drink plenty of water throughout the day. Eat a protein rich diet to maintain as much muscle as possible. Whole grains, omega 3's, all vitamins should be taken. Supplements may be necessary if you can't get them due to the calorie restriction.
Whatever you do don't stop eating all together or eat barely anything because that won't help too much. The metabolism will slow and it will become counterproductive and your body will start eating the muscle for energy.