In 2005, McGeechan was in charge of the midweek team - the "dirt-trackers" - which travelled through New Zealand unbeaten while the Test team were humbled 3-0 by the All Blacks.
He left a lasting impression on Williams, whose only previous experience of McGeechan had been from watching the famous behind-the-scenes documentary of the victorious 1997 tour to South Africa.
"I got on very well with Geech, I thought he was great," said Williams. "There were times he stood up to deliver a speech and it was overwhelming. It made the hairs on the back of your neck stand up.
"Those team-talks and how he made me feel before going into games are the things I remember most about the tour. Motivationally he is one of the best you will come across.
"He is a very good speaker, he is a very good people person. He was one of the coaches I got on with most on tour and it is great he is involved again.
"He is a very experienced coach, manager, player. You name it, he has done it. He is an ambassador to the Lions."