It might help calm the nerves of a skipper, who immerses himself in every aspect of his job with extraordinary intensity, on the eve of the all-or-nothing test match that could define his captaincy career.
"His Holiness, do you have any good meditation techniques to fall asleep?" Smith asked.
The Dalai Lama replied: "That I don't know.
"I think indirectly when your mind is at peace, then sleep automatically or naturally comes.
"If your mind is much disturbed and too much anxiety, too much anxious and too much stress and anger of course ... these are very bad for sleep.
"So relax your mind and go there. Usually, I spend nine hours sleep, very peaceful.
"Around 6pm sleep then 3am wake-up. Then, at least four hours for some meditation."
Smith said later that the Dalai Lama can help Australia create history in India.
"He gave me his blessings. We rubbed our noses together," said Smith. "Hopefully, it'll help me with my sleep over the next five days.
"It just relaxes us a little bit. He's all about compassion and oneness for each and every human being, and it was great to hear something like that from someone as prestigious as the Dalai Lama.
"It was a great experience for all of us. We get over the top sometimes when we are out there playing cricket, but at the end of the day, it's just a game and you need to realise that at times.
"That's something this team can take from meeting with the Dalai Lama."
When the Dalai Lama opened the floor for questions, the Australians hung off his every word. David Warner, who is an avid disciple of meditation and positive thinking, opened up.
"How do you improve your peace of mind?" Warner asked.
The Dalai Lama replied: "You yourself [should] experiment. "The day you met some of your trusted friends and spent some moment for lunch or a few drinks, I think that day you feel happier.
"And then one day, you see you met someone, you feel uncomfortable, the whole day you feel not very happy. So, physically, nothing has changed, but mentally it makes differences.
"So peace of mind is very, very important. I think animals, they have no language, but they also love peace of mind.
"Since we have this remarkable brain, now you must [use] this brain for further strengthening of basic human values."
But on the topic of cricket, his Holiness offered: "I know less than zero."