What method should be used for caramelizing chopped lime

The classic way to make a caramel sauce is to cook approx (this is what we use at the restaurant, because sometimes we get distracted and have to run away; it's more forgiving. Use less water if you can concentrate) 4:1 sugar:water until the sugar has taken a golden colour. Remove from heat, whisk in cream and butter until you reach your desired consistency, add a pinch or two of salt, just enough so you can taste it. This will get you a nice caramel sauce, keeps a week or so at room temp.

Edited to respond to question:

Honestly, I have no idea what the ideal ratio is. I just do it by feel. There should be a zillion caramel recipes available via google that can be more specific. Offhand I would kind of sort of guess that for three cups sugar I use roughly 3/4c cream and 3tbsp butter. Ish.

Edited to provide another answer:

If you wish to use condensed milk to create something that will be closer to a dulce de leche, do the following. This can be extremely dangerous, please be sure to follow all directions. I am not responsible if you injure yourself:

Fill a large pot with water. Keep another pot boiling for topping off the main pot as water evaporates.

Place a can of condensed milk, still sealed, label removed, into the main pot. Bring up to a hard rolling boil. Top up the water as needed. Ensure that the can is always covered with at least six inches of water. Keep a lid on the pot, just in case.

Boil hard for four hours. Turn off the heat, and allow the water in the pot to come slowly down to room temperature. Do not at this point touch the can.

After cooling, let the pot continue to sit at room temperature for at least one hour. At this point, reach into the pot and gently touch the can with your hand. If it is still warm, leave it to cool further.

Once the can is completely cooled to room temperature, you may open it. If you want to be sure, leave it overnight.

You will have a glorious caramel sauce.

Note: I have intentionally described this process with significant margin for error for safety. There will be significant pressure inside the can, and opening it prematurely can very easily result in life-altering injuries.

The secret to really crispy skin has everything to do with rendering the fat that lies directly under it. Once that fat has removed itself from the skin, a little high heat will crisp it up perfectly. If I am creating a roast chicken, I normally remove it from the packaging and allow it to sit uncovered in the fridge for at least overnight, longer if I have the time. Then I start the chicken low to render the fat, you have to cook it at a minimum of 178F (80C) to remove the most fat. Once the fat renders out, which is going to vary depending on the temp you start the chicken at, you crank the temp to the 450 to 500F range and baste regularly.

To maximize the skin that will crisp you want to make sure that your chicken isn't sitting inside the fat while it cooks. I normally use a inset rack to keep the chicken above the fat but you don't have to. The other component to crispy skin is cooking the chicken uncovered.