Mr. Berlind worked on over 100 Broadway shows- spanning nearly 45 years- and won himself a stunning 25 Tony Awards (more than Hal Prince, according to this article). I don't think anyone on these boards will be surprised if he is awarded a posthumous Lifetime Achievement Tony.
Not to diminish his death, but comparing him to Hal Prince is like comparing apples and oranges. Hal won most of his 21 Tonys for directing or being the SOLE or LEAD producer of his shows. I'm pretty sure that Roger Berlind was the sole lead producer on only a few shows. His contribution to Broadway is great, but I would be shocked if he got a Lifetime Achievement Award.