The Begum Shahi Mosque is the oldest surviving Mughal mosque in Lahore — built in 1614 by Emperor Jahangir for his mother Maryam-uz-Zamani. It sits inside Akbari Gate (now Kashmiri Gate) on the eastern edge of the Walled City. The exterior is plain red brick; the interior holds spectacular Mughal frescoes on the prayer-hall ceiling that survive in fragments.
The mosque is much less visited than the Wazir Khan or Badshahi mosques, which means you may have the courtyard to yourself. Access for non-Muslims is usually fine if you observe the standard modest dress and remove shoes; ask before photographing the interior.