The third Test between the Lions and All Blacks at Eden Park will go ahead as planned on Saturday, but a minute's silence will be held before kick-off.
Lions players and officials with family and friends in London were able to contact them overnight, and at this stage none of the touring party has been directly affected.
"Our thoughts are with all those in the UK who have been affected," said Lions tour manager Bill Beaumont.
"As far as can be established at this stage, we are fortunate that none of our touring party have had family or close friends directly affected, although we will continue to monitor the situation."
Thousands of Lions fans are currently in Auckland for the Test, and they too were attempting to make contact with friends and family.
New Zealand Rugby Union deputy chief executive Steve Tew added: "We are saddened by the events in London and want to extend our sympathies to the families of those killed, and to the many injured by these attacks."
All Blacks coach Graham Henry began his final pre-match press conference by also offering his sympathies.
"We would just like to pass on from the All Blacks our deep sympathies to the people affected by the terrorist attacks in London," Henry said.
"The game, really, doesn't seem that significant when these sort of things are going on in the world."