Under which all circumstances is lying permissible (especially lying to parents; especially when they tell you to do something which is not in accordance to Islam - such as girls not allowed to go out to seek Islamic knowledge)?

Praise be to Allah, the Lord of the World; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

No doubt that lying is prohibited by the Qur'an the Sunnah and the consensus of all Muslim scholars. It is a characteristic of the hypocrites. So, it is not lawful except in three situations:
1) During war as war is built on stratagem.
2) The talk of a husband to his wife and of the wife to her husband if that talks leads to good company and the like.
3) Lying in order to settle problems between people.
So, you are not allowed according to Sharia to lie on your parents in order to attend religious lessons. You should talk to them and explain to them frankly what you need above all if this knowledge is an individual obligation on you. But if it is a communal obligation and your parents prevented you from attending its sessions then you should obey them as obeying one's parents is an individual obligation and the individual obligation is given priority over the communal one.
Allah knows best.