Lambert insists he has always had a "good relationship" with Lerner and Villa chief executive Paul Faulkner.
He said: "I trust Randy. That's the kind of relationship I have with him.
"I spoke with him after the game the other night and we have a good conversation every time. I have a good relationship with him and Paul. Randy and Paul have been great with me.
"But I also know the realism of football. That's one thing I will never shy away from. I also know what can happen and what doesn't happen in football. You've got to get results.
"People say it's nice to hear your job is safe. I don't think anything is set in stone in football. I know everything can turn and change.
"But, as I've said, I get on really well with Randy and Paul. As long as people are clear with me and have face-to-face value, I don't have a problem - never."