Sorry for the late reply. We were on vacation and just returned to the office an hour ago. Anyhow, you need to complete a deathless run for that exact key. More specifically, you must reach the pyramid you can enter after completing all the tombs without a single death (tomb deaths don't count). If you cannot do this on your current save, there is always the NG+ option we added in the last patch.
The door is just left of the link tower in Sunburn Desert.
What a pity I did not know about that earlier... Thank you for responding to that user's post. I found this useful myself.