Actually the most up to date figure for the tower is now at 858' so we already have a whopping 7' height bump from 851'!
https://www.relatedmidwest.com/our-company/properties/400-lake-shore
https://chicago.urbanize.city/post/400-lake-shore-drive-scores-full-building-permit
https://www.costar.com/article/127012383...-a-little-shallower-as-new-plan-proceeds
CBTUH still seems to be using 850' though (which I think was the original north tower height with the other one being 1100')