Robertson guided the Crusaders to the Super Rugby Aotearoa title earlier this month to add to their three successive Super Rugby titles since he took over in 2017.
He missed out on the All Blacks coaching job last year and said he had approaced Lions and Chiefs coach Warren Gatland about a role on the Lions tour to help give him some international experience.
"I thought, look if I can't be involved with the All Blacks, what's the biggest thing - or actually bigger in its own self - the Lions tour - to get involved," Robertson told New Zealand radio station Gold AM.
