I've decided to break it down for you.
I see that you are a 20 female from your post history. Great.
I'm going to assume you are 5'5". If you are average height or lower this will be an overestimation of how many calories you burn. You're welcome.
"Slightly overweight" is about 160 pounds at your height. Lets assume you are underestimating and are 170. Again, this will only work to your advantage in my calculations.
20/f/5'5"/170lb equated to a BMR of 1600 calories. This is how many calories your body burns without exercise. Unless you are 5'5" or taller or 170 or heavier, your true BMR is less than this.
You "go to the gym" for one hour a day.
You have now burned up to 2000 calories today.
In order to lose only 2 pounds per month as you claimed, you would have to have a caloric deficit of 7000 calories per month or 230 per day.
This means you are eating 1770 calories worth of carrots and lettuce (coffee doesn't have calories).
Carrots: 100g = 41 calories
Lettuce: 100g = 15 calories
Lets say its equal amounts of each.
3000g x 41 cal = 1230 calories from carrots
3000g x 15 cal = 450 calories from lettuce
Thats 1680 calories. In order to lose only 2 pounds a month on 1 hour of exercise per day eating only lettuce and carrots, you need to eat 3 kg of carrots and 3 kg of lettuce every day. Thats 6.6 pounds of each.
Now, a more likely story is that you ate:
a bagel with cream cheese (320 calories)
orange juice (1 cups 110 calories)
a salad (carrots and lettuce) with 3 tbsp of ranch (240 calories)
and croutons (10 for 50 calories) for lunch,
2 cups of coffee with cream and sugar (100 calories)
pizza (2 slices 700 calories)
potato chips (1 cups 170 calories)
diet soda
and your 1 hour of exercise was yoga (220 calories)
That's 1820 calories out and 1690 in. You'd loose a bit less than 2 pounds a month.
That's not a bad diet or exercise program, but it won't make you shed pounds. 2 pounds per month is perfectly healthy and admirable. Lying about it is not.