It was a victorious end to a turbulent week which saw former manager Dougie Freedman move to rivals Bolton with Lawrence and Curtis Fleming put in temporary charge at Selhurst Park.
After goals by central defenders Damien Delaney and Peter Ramage set up their stunning 2-1 win, Lawrence said: "We knew exactly how difficult it would be at Leicester who will be in the top six at the end of the season without a shadow of a doubt.
"We had a game plan and it worked. We started boldly and scored two goals whereas at Barnsley we just got one.
"We knew they'd throw everything at us and they did but we defended resolutely, Julian Speroni made some saves and we rode a few moments of luck.
"Whoever takes charge will have a side that has every chance of maintaining a
play-off challenge. They are so good as a unit, they could probably run themselves for a week or two.
"They have been absolutely spot on since Dougie left - if they weren't, you could never come to a place like this and win."