The players arrived in Dharamsala on Thursday evening and opted not to practise on Friday, instead choosing to take to Himalayan foothills where the Tibetan spiritual leader is based.
The squad, as well as a handful of support staff, attended the Buddhist temple complex at McLeod Ganj, around 15 kilometres from the team base.
The group headed to the hills in two buses to take in a visit far removed from their normal programme of hotel restaurants and fielding drills.
England stayed for half an hour but did not meet the Dalai Lama, although there is a chance they still might at the fifth one-day international on Sunday.
The Dalai Lama's office confirmed to Press Association Sport that the fixture is not currently in His Holiness' diary but said that it was still possible he may make an appearance at the city's first ever international match.
It would not be his first taste of top-level cricket. Indian Premier League franchise Kings XI Punjab use the HPCA Stadium as one of their home venues and the Nobel Peace Prize winner attended matches in 2010 and 2011.
Batsman Kevin Pietersen offered a glimpse of the trip as he posted a picture on Instagram of himself in front of a painting of the Dalai Lama, writing: "His Holiness himself.. Such an interesting morning visiting his residence!"