In a medium saucepan, combine the brine mix and 2 cups water and bring to a boil. Reduce to a simmer and cook for 5 minutes. Remove from the heat and allow to cool for 10 minutes. Stir in the ice water and lemon juice. Allow to cool completely.
Place the pork in a chicken brining bag or a nonreactive bowl. Pour the brining liquid over the pork. Seal the brining bag or cover the bowl securely and refrigerate overnight.
In a mixing bowl, toss together the crumbs, onion, sage, thyme, pepper and salt. Pour the broth and butter over the mixture and stir well. Refrigerate until ready to use.
Preheat the oven to 400 F.
Remove the roast from the brining mixture and rinse. Unroll the roast flat on a cutting board and spread it evenly with the cornbread mixture. Roll the roast up lengthwise, jellyroll fashion. Tie it at intervals with kitchen twine. Place the roast in a shallow roasting pan, seam-side down.
Combine the vinegar and oil. Baste the roast with the mixture. Roast for 1 hour, or until the internal temperature reaches 155 F on an instant-read thermometer. Remove from the oven and let it rest for 15 minutes before slicing. Cut into 1/2-inch slices to serve.