Combine the hearts of palm, orange sections and juice, tomato, red onion, cilantro, chile, vinegar, and olive oil, and keep chilled until ready to serve. Just before serving, season with salt and pepper.
Place the split lobsters on the grill, flesh side down. Cook for 5 to 6 minutes and then turn over and cook for 5 to 6 more minutes.
Place the lobster on serving platters filling in the top, empty part of the shell with the slaw.