The towering second-row broke a thumb in last weekend's one-point Super Rugby loss to the Crusaders.
Following consultation with specialists, it has been decided that Timani requires surgery and he will now miss the entire Test series with Warren Gatland's men.
Meanwhile injured Melbourne Rebels loose forward Scott Higginbotham has undergone scans after dislocating his right shoulder last Saturday. The Rebels captain will be reassessed later in the week.
The duo have both been replaced in the Wallabies squad, with Waratahs lock Kane Douglas and Western Force backrower Ben McCalman coming in.
Robbie Deans' Wallabies are currently in camp preparing for the mouth-watering series with the Lions.
The current squad of 25 will be extended to 31 with six players added to the party on June 11.
Brumbies scrum-half Nic White will train with the squad on Wednesday and troubled Melbourne Rebels fullback Kurtley Beale is also in camp.
Beale returned to action for Randwick in the Shute Shield clash against Sydney University on Saturday, two weeks after counselling for alcohol-related issues, and two months after a suspension for hitting Rebels teammates Gareth Delve and Cooper Vuna.
And ARU boss Bill Pulver reckons the controversial star can go on to become a role model and icon of Australian sport.
"Kurtley Beale is a national treasure, and we're doing our utmost to help him through a tough situation," said Pulver.
"Step one is for him to get control of his life again, make sure that he has a healthy and wonderful future as a fine young man.
"If as part of that he can get his rugby career going again, that would be a fabulous thing for the game.
"I want Kurtley Beale out there as the role model for other indigenous athletes to come through and play at the elite level of our game. Kurtley Beale is the modern-day example of a wonderful kid, the rugby community has dined out on that kid since he was 12, ever since he stepped out for St Joseph's College.
"As a game, we sadly have a relatively low population of indigenous players at the elite level."