Whisk together the flour and egg in a medium bowl and gradually add the milk and then add then the chives and stir to combine and season with salt and pepper.
Lightly grease a large non-stick pan and place over medium heat.
Spoon five tablespoonful quantities of mixture into the pan, allowing room for spreading and cook for 1 to 2 minutes or until golden underneath and bubbles appear on the surface and then turn and cook for a further 30 seconds or until golden underneath and transfer to a plate and repeat with remaining batter in 3 more batches.
Place the blinis on a serving platter and smear a dollop of sour cream and top each with a slice of lobster then the avocado that have been mixed with the lime juice.
Top the each with a sprig of dill and serve with lemon, if desired.