Remove lobster from the shell. Devein and cut lengthwise in half. Season with salt, pepper, lemon juice, and brandy, and allow to marinate for 30 minutes.
In a saucepan over medium-low heat, melt half of the butter and saute the shallots until they turn clear. Add flour and make a light roux.
Add the ginger and the chicken stock and reduce over low heat to half the original volume.
Meanwhile, with a sharp knife cut a pocket in each of the chicken breasts. Slice the lobster tail on the bias into three pieces. Stuff the lobster inside the chicken, making sure that the lobster is surrounded by chicken meat.
Season chicken with salt and pepper. Put it on an oiled baking pan or in an ovenproof skillet. Pour the wine over the chicken and place the skillet into a preheated 300-degree oven for 20-30 minutes--until chicken is cooked all the way through.
After the sauce is reduced, whisk in the rest of the butter, one chip at a time. Adjust the seasoning with salt and pepper. (Note: this should not be a spicy dish.)
When chicken is cooked, pour off juices from the pan into the sauce and blend in. Slice the chicken breast to get a disk of lobster in the center. Spoon sauce onto the plate and place slices of the chicken/lobster on top.