Is it permissible to take a mirror found on the ground at the Miqat, when one needs it to adjust her hijab, knowing the prohibition for a pilgrim (Hajj or Umrah) to pick up lost property (Luqata)?

There is no harm in picking up the mirror because it is a minor find that the average person would not bother with, and it does not need to be announced. This is based on the Prophet, peace and blessings be upon him, who permitted picking up sticks, whips, ropes, and similar items for personal use. He also passed by a date and said, "Were it not that I fear it might be from charity, I would have eaten it." Your being in a state of ihram (definition) does not prevent you from picking it up, because the prohibition of picking up lost items except for the purpose of announcing them is specific to the sanctuary of Makkah, as the Prophet, peace and blessings be upon him, said: "Its lost item should not be picked up except by one who will announce it." If you were at the Miqat (definition), this ruling does not apply to you. Even if you picked it up in Makkah, it is permissible, because the ruling for Makkah regarding minor lost items is the same as elsewhere.