is key lime juice the same as lime juice?
You mention lime and dark spots on the peppers, which makes me wonder if you are dealing with blossom end rot. Is the dark spot on the bottom end of the fruit? If that is the case there can be several other causes besides a soil pH imbalance. Irregular watering, excess nitrogen or potash fertilizers can also bring about the calcium deficiency that caused BER. Lime is only used to raise pH if the soil is acid. It is not necessarily a cure for BER. If the brown spots are caused by a virus, lime isn't going to help, anyway. You really need to do a soil test before you just start dumping line in your garden.
The dark spots on your peppers is a viral disease. Without a picture or more info I can't tell you which one it is.There are a few diseases that effect peppers. Some live in the soil and some don't so don't plant them in the same place next year. Is the plant infected too. Is the spot soft and squishy or hard. Is the spot on the end or in the middle of the pepper. Adding lime is best done when there is nothing planted in the spring. You just sprinkle the agricultural lime on top of the soil and work it into the soil. It's best if it's watered or has a rain before you plant