Table was not locked with LOCK TABLES when recreating an index
Try creating a temp table, and then perform a bait-and-switch

ALTER TABLE stuff RENAME oldstuff
CREATE TABLE newstuff LIKE oldstuff;
ALTER TABLE newstuff DROP INDEX idx_UpdatedTime;
INSERT INTO newstuff SELECT * FROM oldstuff;
INSERT INTO newstuff (x,y,z) SELECT x,y,z FROM inventory;
ALTER TABLE newstuff ADD INDEX idx_UpdatedTime(UpdatedTime);
ALTER TABLE newstuff RENAME stuff;
DROP TABLE oldstuff;


This approach may take longer but should establish some continuity for your processing

I renamed stuff to oldstuff to remove any possibility access to the stuff table during this process