Is it permissible to respond to someone who calls me "Labbayk," or is this word exclusively reserved for the Lord of the Worlds?

There is no harm in answering someone who calls with "Labbayk," and the scholars have not mentioned that answering with it is exclusive to Allah Almighty. A number of Companions, such as Mu'adh ibn Jabal, Abu Dharr, and Bilal, answered the Messenger of Allah, peace and blessings be upon him, with it. Al-Bukhari and Abu Dawud titled chapters on its permissibility. Umar ibn al-Khattab and Amr ibn al-'As also answered with it, and Abu Bakr answered Bilal with it.