Lockwood slammed home his eighth goal of the season after Scott Brown pulled down Adam Chambers in the area.
But City hit back six minutes later when Phil Jevons raced down the right and cut the ball back for Johnson to fire into the corner of the net as the visitors stretched their unbeaten run to nine league games.
In an enthralling first half both sides prompted and probed with some clever approach play, but clear-cut chances were few and far between.
But it was the visitors who could have grabbed a second minute lead when Orient striker Gary Alexander under-hit a back pass that allowed Enoch Showunmi in but Glyn Garner pulled off a smart save.
Garner was in action shortly afterwards when he brilliantly tipped away Bradley Orr's drive from distance.
But the home side hit back and Alexander fired over before City keeper Adriano Basso parried away a fierce drive from on-loan striker James Walker.
As both sides strove for an opening it was City who went close before the break when Jamie McAllister fired in a free-kick from 20 yards that whistled passed Garner's right-hand post, then Scott Murray's 20-yard drive was saved by the Orient keeper.
After the break the Robins started well before Orient came back into the game and Alexander headed inches over the bar.
Then the home side underlined their superiority when Lockwood fired home from the spot.
But City, on an impressive unbeaten run, were soon back on terms following Johnson's clinical strike.
After that both sides had chances to win the game but it was Orient who were left kicking themselves for not making the most of their opportunities.
The home side should have restored their advantage 15 minutes from time when the ball fell neatly into the path of substitute Jabo Ibehre, but his tame shot from 12 yards was saved by Basso.
Then from a Luke Guttridge free-kick, fellow substitute Paul Connor toe-poked an effort just wide of the post.