Preheat the grill or pellet grill on MEDIUM heat 400°F (204°C). On the left side of the grill place a large skillet or roasting pan. Drizzle olive oil in the pan then the onions and peppers. Place sausages directly on the cooking grates on the opposite side to grill, flip them to prevent charring. Stir peppers and onions often until the onions start to caramelize.
Add beer and spices to the peppers and onions. Grill sausages for 20 minutes until they are cooked then cut them into slices and add them to the peppers and onions. Grill the lemon halves, face down, until they are golden brown. Squeeze in the juice from the lemon, remove the seeds then add the lemon halves, stir. Peppers and onions should take around 30 minutes to cook and soften appropriately.
Toast the buns or bread on the warming rack in the final minutes. If serving with cheese, add sausage and peppers mixture to the bun the top with shredded cheese and leave on the warming rack to melt the cheese.