Preheat the oven to 150 degrees C / 300 degrees F.
In a medium saucepan on a low heat, add the butter and begin to stir or whisk frequently. Once melted, the butter will begin to foam and sizzle. Add the lemon slices and onions to the pan with the butter and continue to stir for an additional 5 minutes or until the butter turns a golden brown colour and has a nutty aroma. The milk solids will fall to the bottom of the pan. Add the capers to the butter and stir through. Immediately take the butter off the heat.
Lay the salmon onto a large baking tray and season generously with salt and pepper. Drizzle with olive oil. Pour the brown butter mixture all over the salmon and bake for 15 – 20 minutes.
Sprinkle with dill all over and serve immediately.