To make the champagne sauce, simmer shallot and champagne in a saucepan over medium-high heat for 4-5 minutes until shallots are tender and champagne is reduced by half. Add the cream, simmer for 5-6 minutes until sauce is thickened. Stir in butter and vinegar to combine and emulsify, season to taste and keep warm.
Combine melted butter, chilli, garlic and lemon rind in a small bowl, season to taste.
Heat a barbecue or char-grill pan to medium-high. Brush cut sides of lobster with a little garlic butter, season to taste. Place lobsters cut-side down on the barbecue and grill for 3-4 minutes until shells begin to change colour. Turn and brush with a little more garlic oil butter. Grill for another 3-4 minutes until flesh turns opaque and transfer to a plate.
Add asparagus to the grill and grill until just wilted, remove from the heat.
Arrange the avocado on a platter with lobster and asparagus. Drizzle with a little champagne sauce, scatter with herbs and serve with lemon wedges.