I think you're interpreting the story incorrectly.
Rex is not presenting what he said to Lynn as fact, or that he has some secret insight to the future...
He is presenting an opinion...
No one knows what is really going on with the team better than Rex, and I'm sure he was predicting trouble before the season ever started. Don't forget that behind the scenes Rex (real Rex) has nothing to do with the Rex we see and hear.
I interpret the story to be Rex having come to terms with his fate, realizing this is going to be a bad season and he is unlikely to survive it, combined with a short history of events, comments, discussions, etc., that suggested to him that Lynn was very highly regarded by the Pegulas, such that he would be the likely choice as at least an interim coach.
And in fact, Rex may well have a say in that too. I can totally see an amicable split even if Rex is fired whereby he is asked for his input regarding who a good interim coach would be.
Anyone at that level would likely be professional enough to suggest someone and not want to hold back that person's career while simultaneously leaving the organization themselves.
This is simply Rex saying "Who are we kidding here? We are going to be bad this year and I'm not going to survive. And Lynn, you are as well liked as anyone in the organization to replace me when I get axed. So think wisely before you leave the organization."