A girl and a boy is married in the Nikah ceremony. But the banquets of marriage (the girl is in her parents' house) will take place in 4 - 6 months. Is it lawful for them to have sex? Please elaborate on your answer.

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.

After completing the marriage contract between a man and a woman she becomes his wife. Thus, it is permissible for each other to talk, to be alone and do whatever a husband and wife do. However, it is a common practice among people not to establish intimate relations with a wife till conducting the marriage ceremony. Therefore, it is better to follow the custom. However, a person can talk with her wife (fiancée) after completing the marriage contract even if the family of fiancée denies it, since there is no sound basis for their refusal. Even though, the fiancé should be patient and deliberate considering the feelings of the family of fiancée. The Prophet (Sallallahu Alaihi wa Sallam) said: "Verily Allah is kind and He loves kindness and confers upon kindness which he does not confer upon severity" . [Ahmad, Abu Dawood, Ibn Majah, and Ibn Hibban in his Sahih].
The fiancé and fiancée should avoid any kind of disagreement with her family as it may lead to bad consequences.
Allah knows best.