I am breast feeding 2 month baby. Is drinking warm water mixed with honey and lemon, empty stomach a good idea for me in this situation?

Breastfeeding diet. It is okay to do so. But make sure you also take in a well balanced diet with additional protein and dairy in your diet. Warm water with lemon and honey helps to lose weight according to some ethnic beliefs. It should not do any harm. Honey is oaky for you but not for baby to be fed directly. Keep up the breastfeeding!
Should be fine. This would be fine for you if you enjoy the beverage. We do not recommend baby have honey the first year to avoid a source of botulism germs, but your system is not at risk and your milk would not pass it to baby.