I also believe that (much like Titan Runestones) there is a guaranteed drop from Lei Shen.
I only picked up the quest last week and had a total of 9 Secrets after a full clear (compared to others I believe I have been quite lucky). This week I have done the first 4 of SoO on flex and acquired another 2.
However since patch 5.4 after a full clear of ToT LFR the only boss to drop a Secret of the Empire was Lei Shen. I have read many other posts of people mentioning the same thing. Can you please confirm/deny that the drop rate is currently bugged?
N.B. I have NOT done ToT on normal/heroic for this lockout.