You didn't specify your MySQL server version or table engine, but if you're on InnoDB using a recent version of MySQL (> 5.6), have you considered using explicit Online DDL?
ALTER TABLE main_table
ADD `last_updated` DATETIME DEFAULT CURRENT_TIMESTAMP,
ADD INDEX (`last_updated`),
ALGORITHM=inplace,
LOCK=none;
Note that there are some constraints on when the in-place algorithm can be used.
If you have foreign key constraints in effect, disable those or the copy algorithm will be used. And it'll be slow.
If your table was created pre-5.6, then you'll need to rebuild the table using a copy algorithm before you can switch to the inplace algorithm.
Finally, if you're using pre-5.6 or these don't work for whatever reason, consider using Percona's online-schema-change.