NativeNYer2 said: "Lee Grant is still alive and she never won a Tony award. She also might make a good recipient for this award."
If you look at Lee Grant's data on IBDB.com, you will understand why she has never won a Tony Award. She was last on Broadway 52 years ago, in Prisoners of 2nd Ave, in which the male lead has the meaty role. Prior to that, beyond a show that ran less than a week, she understudied and took over the role of Gittel Mosca in Two for the Seesaw, in 1959, i.e., 65 years ago. Prio to that, other than Detective Story, in which she played a supporting role, there is nothing to suggest any justification for a Lifetime Achievement Award.
Looking at the lists, it seems to me that 3 women belong at the top of that list: Alexander, Lupone and Peters Re males, Tom Stoppard's name was raised last year, and should still be on the list