Villa have made a torrid start to the Premier League campaign with just one victory to their name, and even that win came way back on the opening day of the season.
Sherwood's men are rooted in the relegation zone right now, and desperately need a result as they take on an out-of-form Swansea City side today.
The Swans lost 1-0 at home to Stoke City on Monday night, meaning their last win came on August 30th against Manchester United, with Garry Monk now going six games without a victory.
It's a vital match for both managers, with some believing that Sherwood could lose his job if he fails to claim a victory - and that's something that BBC pundit Lawrenson claims he has heard.
Lawrenson has told BBC Sport that he believes Aston Villa and Swansea will draw at Villa Park this afternoon, with the two game mattering too much to both managers for them to gung-ho and risk losing the match.
Lawrenson also believes that questions over Sherwood's future are crazy considering that he not only kept them up last season, but also took them to the FA Cup final, suggesting that he deserves more time despite a poor start.
"I am hearing that defeat on Saturday might mean the end for him despite what he achieved at the club last season," says Lawrenson. "It is a mad world we live in but it means neither manager can afford to lose on Saturday. Consequently, I am going to go for a draw and see what that means for them," he added.