Heat oven to 250°F. Have two separate large baking pans or baking sheets and a candy thermometer ready.

Combine vegetable oil and popcorn kernels in a medium saucepan over medium heat. Cover, leaving a small gap for the steam to escape.

Cook, shaking occasionally, until the sound of popping corn slows to a stop. Immediately pour popcorn out onto one of the baking sheets and let cool slightly, keep saucepan close by, you will use it again to make the caramel sauce.

Go through the popcorn and pick out any kernels that didn't pop or ones that aren't fully popped. Then transfer the rest to the other baking sheet.

In the same saucepan, attach a candy thermometer to the side and melt the butter over medium heat. Add brown sugar, juice, and salt and bring to a boil, stirring to dissolve the sugar.

Continue to boil until the temperature on the thermometer reaches soft boil stage, or 235°F, about 8 minutes.

Carefully pour the caramel over the popcorn and stir to coat. Spread out into a single layer and transfer to the oven.

Bake for 1 hour, stirring every 15 minutes. Lay a large sheet of foil or parchment paper on the counter and turn the caramel corn out onto the foil to cool.

Have a baking sheet lined with paper towels ready. Heat oil in a deep pot or Dutch oven to 350°F. Add half the chicharrones and fry, gently stirring so they cook evenly. When they are opened and cooked through (about 1 minute), remove with a bamboo skimmer or slotted spoon to the paper towel-lined baking sheet. Repeat with remaining chicharrones.

Toss caramel corn, chicharrones, peanuts, and almonds together in a large bowl. Squeeze lime juice over everything and serve immediately.