Players visited a site in London on Wednesday to be given the Pfizer jab with only Scotland stand-off Finn Russell missing as he is based at Racing 92 in Paris and has already been vaccinated.
The Government approved the move to protect Warren Gatland’s squad ahead of their visit to South Africa a red list destination that is seeing a growing number of coronavirus cases.
In the wider population, only people aged 30 or over are currently eligible for a jab.
The Lions hope all 37 players will get their second vaccinations by the end of their pre-tour training camp in Jersey, which begins on June 14 and leads into the warm-up game against Japan at Murrayfield on June 26.
Gatland and his management team are already advanced in their vaccination programme.
It is still not known whether the Lions will be required to quarantine for 11 nights in a Government-approved hotel when they return from South Africa on August 9.
Discussions over receiving dispensation on the basis they will be operating in a bubble environment are ongoing.
Russell is one of eight Scotland players have been selected for the Lions tour. The others are Stuart Hogg, Chris Harris, Duhan van der Merwe, Rory Sutherland, Hamish Watson, Ali Price and Zander Fagerson.
The Lions will play three Test matches in South Africa on July 24 and 31 and August 7.