Carlisle, chasing a play-off place, took a 15th minute lead when Joe Garner headed home, but Lockwood fired an equaliser at the start of the second half as honours ended even.
Orient had made a bright start after two successive defeats and on-loan striker Ryan Jarvis from Norwich almost opened his account on four minutes.
Shane Tudor danced down the right and sent in a cross but the young striker saw visiting keeper Keiren Westwood parry his first effort and block his second.
But then the visitors broke away and scored with their first effort on target on 15 minutes.
Jeff Smith sent in a corner from the right that was met by Garner who lost his marker and sent a header into the roof of the net from six yards.
Orient hit back and striker Gary Alexander saw a header drift on to the bar on 31 minutes following Wayne Corden's free-kick.
Despite Orient's pressure, Carlisle looked dangerous on the break and the highly impressive Kevin Gall went close with a speculative effort from 40 yards with Orient keeper Glyn Garner stranded.
Carlisle's top-scorer Karl Hawley then saw an effort cleared off the line by Orient skipper John Mackie when he really should have added a second.
Tempers began to fray as the first half came to a close and Orient duo Lockwood and Corden both went into the book.
At the start of the second half both sides made changes but it was Orient who were level within 90 seconds.
Lockwood rifled home past Westwood from a tight angle after Carlisle defender Zigor Aranalde had headed away a corner.
After that Carlisle weathered the storm and chances were few and far between before Orient pushed forward in a late bid to nick all three points.
The closest they came to grabbing a second arrived when Adam Chambers went close with a header that slipped the wrong side of the post, while Jarvis tried a snap-shot from 25 yards that Carlisle keeper Westwood failed to hold.