Leicester take on Harlequins this Saturday with George Ford on standby should Flood fail to recover in time.
But despite his public outburst last week after Lancaster revealed Flood was in doubt for England's summer tour to South Africa, Cockerill insists that all is well between the two of them.
"Me and Stu didn't have a bust-up," he said.
"We met last week and had a discussion about how we will handle things in the future. I get on with Stu.
"We have a good relationship. We had a difference of opinion, which is okay. We had a healthy discussion and worked out a way of dealing with things moving forward."
"Floody is working hard and improving day by day."
Saturday's Twickenham showpiece marks Leicester's 12th final in the last 14 years, a remarkable run that takes some beating in any sport.
But after a disappointing start to the season that saw the Tigers lose six of their first seven games a final-berth looked a long shot to most people, just not Cockerill.
"I was confident we could get the season back on track," he added. "To what degree, I never knew.
"Normally, we have a good start to the season and can afford a slip-up here or there. But having lost six of the first seven games, there was no opportunity to lose.
"We had to pretty much win every game and that's what we have done barring one. The turnaround has been good. Was I sure it would be this good? I could never say that, but I will take it."