Prepare the barbecue for direct cooking over medium-high heat (200°C to 230°C).
After the crayfish has been put to sleep, using a large sharp knife or cleaver, cut the crayfish in half lengthways, through its head and tail. Scoop out the yellow/brown tomalley and remove the intestinal vein. Lightly coat the flesh with olive oil and season with salt and pepper.
Add the chorizo and garlic to a Weber frying pan. Place the frying pan onto the cooking grill, close the lid and cook for 4 to 5 minutes over direct medium-high heat, stirring as needed, until the chorizo has started to caramelise and the garlic has cooked. Remove the frying pan from the barbecue and stir in the butter and oregano, set aside, leaving the butter to melt.
Place the crayfish halves onto the cooking grill, flesh side down, close the lid and grill over direct medium high heat for 3 minutes, or until seared. Add the lemon halves to the barbecue, cut side down, and grill for 3 minutes, or until caramelised, set aside until required. Flip the crayfish halves over, onto the shell side. Carefully spoon half of the chorizo butter over the crayfish, close the lid and cook for a further 3 to 5 minutes, or until the crayfish has just cooked through.
Serve the crayfish immediately, with extra chorizo butter and a generous squeeze of caramelised lemon juice.