Both players, along with centre Brian O'Driscoll, sit out Saturday's clash against the New South Wales Waratahs.
Juggernaut wing North reported a tight hamstring during the victory over a Combined Country XV on Tuesday, while Tuilagi is recovering from a shoulder knock suffered against Queensland Reds three days previously.
And Lions head coach Warren Gatland has revealed that injuries could play a part when it comes to selection for the opening Test in Brisbane.
"I think there are one or two that are a little bit sore that may next week be out of contention because they won't have been fit enough early enough in the (Test) week," Gatland said, without naming specific players.
"That is potentially what might happen. By the time Saturday (first Test) comes round, they might all be fit, but one or two are possibly going to be ruled out because they are not fit enough earlier in the week. We've got a few bodies among the backs who have been knocked around, which is why Billy Twelvetrees has been brought in as cover."
Gatland believes that future Lions squads may need to be bigger in number because of rugby's increased physical nature and injury attrition rate. He selected a 37-man party for the current Australia tour, but props Cian Healy and Gethin Jenkins have already gone home injured, wing Tommy Bowe is recovering from a broken hand and full-back Rob Kearney is involved for the first time this weekend after being sidelined by hamstring trouble.
Three players - Alex Corbisiero, Ryan Grant and Simon Zebo - have flown in to join the squad, while Twelvetrees was called up from England's Argentina tour.
"I think that as you move from one tour to the next, you realise how tough it is, especially for the players," Gatland added. "The game's physicality has increased from 2009 (Lions tour) in South Africa. It has stepped up a level, and players handling two games in a week is tough.
"It is something we need to be mindful of. If you are writing a report at the end of the tour, you need to consider whether there is a case for bigger squads from the start because of this step up in physicality."
- Sports & Recreation
- Warren Gatland
- Billy Twelvetrees