I Presume These Rewards Are Mine, Death? is an achievement that requires the player to claim all post-quest rewards from the Missing, Presumed Death quest by speaking to the statue of Death.
Claiming the above rewards will also unlock two new death animations, one featuring Death and one featuring Icthlarin.
If you do not have the required level to claim a lamp, the statue of Death will withhold that lamp and you will receive a message stating that the lamp cannot be claimed. Moreover, all lamps are claimed at once and, as with most experience lamps in the game, they cannot be banked.