Can the timer count up as well as down, and is it possible to lock the timer as it is counting up? Do you have more information about the lock function?

Yes, this will count up as well as down. The timer will count up from 0:00:00 to tell you how long since the alarm sounded. There is also a STOPWATCH feature that will begin counting upward when in "CLOCK" mode. The LOCK feature can only be used when using the TIMER, it cannot be used in STOPWATCH mode. Customer service will be sending you a copy of the operating instructions via email.