The main reason for hair on lower face in females, is hormonal
imbalance. You can go for LASER
hair reduction (go for Diode LASER if you are fair skinned, and NdYAG LASER if very dark skinned). LASER will not give you permanent hair reduction if you have an underlying hormonal irregularity, but it will surely help in reducing the number and thickness of hair, and will also slow down the speed of hair growth.