The Boys in Green face Moldova at the Aviva Stadium on Friday before turning their attentions towards Cardiff. Serbia are favourites to win the group, as they lead Wales by four points.
The injury could not come at a much worse time for Bale for a number of reasons.
As for taking Bale's spot, Lawrence added: "I wouldn't say I can replace him".
"He's fine. After so many games at the start of the season and four months of injury, he was suffering after the game in Dortmund".
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He reported for global duty with the rest of the squad on Monday, and took part in a light training session with the players who featured in the Premier League on Sunday.
The Dragons have won only seven of the 33 games Bale has missed since making his debut in 2006, while Wales have won none of the last 10 when the 28-year-old forward has been absent.
Despite Bale's absence, Bradshaw could well be kept out of the starting line-up by Liverpool teenager Ben Woodburn.
The 17-year-old came off the bench to score the victor against Austria last month.
Only the group winners are guaranteed a place at the World Cup in Russian Federation next year.