Dallaglio, whose 2001 Lions tour of Australia finished prematurely due to a knee injury, will be replaced by Ireland flanker Simon Easterby.
The experienced Easterby, captain of Welsh regional side Llanelli Scarlets, is expected to arrive in New Zealand in the next couple of days.
Easterby becomes the second player in just a few days to answer an injury SOS from Lions head coach Sir Clive Woodward after England lock Simon Shaw was summoned as replacement for Malcolm O'Kelly.
Easterby said: "Obviously I feel for Lawrence, he was looking so impressive so to go out of the tour this way is a massive disappointment for him.
"But I am relishing the chance to be involved in a Lions tour and cannot wait to get out and join the lads in what will be a challenging tour."
The loss of Dallaglio is a major blow to Woodward and his Test match plans, as the Wasps star would undoubtedly have had a pivotal role to play against the All Blacks.
Woodward said: "I am gutted for Lawrence. I know how much this tour meant to him, and he was an important part of our plans.
"But what we can't do is let it effect the rest of the tour, which is why we have called up Simon Easterby."
Gareth Jenkins added: "Everybody is really sad for Lawrence, injuries are part and parcel of the game. This was a big blow but we have a big squad.
"I know with my experience with Llanelli that Simon Easterby is a class player who will rise to the challenge, I have no doubt about that."
Dallaglio now faces a race against time to be fit for the start of the new English domestic season.