Blend the garlic, lemon grass, ginger, coriander, chilli and a little salt in a food processor to make a thick paste. Add the lamb and blend until mixed. Tip out on to the work surface and divide the mixture into 4 pieces. Roll each into a ball and flatten into a burger shape.
Heat the oil in a sturdy roasting pan and fry the burgers on both sides to sear. Transfer to a preheated oven, 200°C (400°F), Gas Mark 6, and cook, uncovered, for 25 minutes until the burgers are cooked through.
Meanwhile, peel the cucumber and cut in half lengthways. Scoop out the seeds with a teaspoon and discard. Cut the cucumber into thin, diagonal slices. Slice the spring onions diagonally. Roughly shred the pak choi, keeping the white parts separate from the green.
Using a large metal spoon, drain off all but about 2 tablespoons fat from the roasting pan. Arrange all the vegetables except the green parts of the pak choi around the meat and toss them gently in the pan juices. Return to the oven, uncovered, for 5 minutes.
Mix together the sugar, lime rind and juice and fish sauce. Scatter the pak choi greens and peanuts into the roasting pan and drizzle with half the dressing. Toss the salad ingredients together gently. Transfer the lamb and salad to serving plates and drizzle with the remaining dressing.