This cannot be done in a group as keys are unique and only one set is given per instance. You need all three keys in your inventory to open the case. Make sure you disband and go in separately or you'll have to do it again!
Zone into Court of Truth's Service Entrance at ( -147, 150, 19 ) /waypoint -147, 150, 19 and complete the following within 10 minutes.
Kill the three Historians (Da'ran, Faz'in, Mandala) in the instance, along with their encounters, and loot the keys from each.
( -0, -0, 2 ) /waypoint -0.06, -0.14, 2.32
( 17, -0, 5 ) /waypoint 17.33, -0.14, 5.16
( -34, -18, 47 ) /waypoint -33.90, -18.33, 47.13
Be careful before clicking on doors! One Historian is in a small room and there is a door behind him. This is the front entrance to the House of Truth. It is possible to zone out of here by accident and then you have to start all over. Don't delete the quest but let the timer run out, otherwise you need to obtain a new key.
Examine the glass casing in the large room on the bottom floor.