Le Guen endured an unsuccessful spell with Rangers - and has since done so in other jobs during his managerial career - with the Frenchman failing to get his players onside at Ibrox.
And Lawwell says this was always a fear that played on the Celtic hierarchy's mind - they knew they had to get over the 'Le Guen hump' at Celtic Park with Deila.
But the chief executive believes the Norwegian has jumped over that initial hurdle with flying colours, suggesting he has got the players on board at Celtic 'brilliantly.'
After a cagey start to his career with the Bhoys, the 39-year-old has guided his side to the top of the Scottish Premiership, into the quarter-finals of the Scottish Cup and the final of the League Cup.
"When we set off with him, we knew we were going to give him time," Lawwell told reporters. "If you go back to Le Guen - I always say to Ronny about the 'Le Guen hump.'
"When he came in, he’d won three-in-a-row in France, had new ideas, a new philosophy and a new culture. It didn’t work. It was revolution rather than evolution. Bang. The players revolted and he went out.
"So we had to get over that le Guen hump if you like and manage through that. You get the players on board and get everything settled down. He’s done that brilliantly."
Celtic were also knocked out of the Europa League by fine margins against Serie A giants Inter Milan, acquitting themselves superbly both in the San Siro and - a few defensive mistakes aside - during the home leg.