The Black Cats are currently 18th and four points from safety.
The Black Cats are currently 18th in the table and four points from safety with just six games remaining.
Sunday did not aid their hopes of avoiding the drop as they were beaten 2-0 by league leaders Leicester City at the Stadium of Light.
With a game in hand over Norwich City above them though, the race looks set to go down to the wire, and both Lawrenson and Sinclair believe they will manage to escape.
"Sunderland will stay up,” Sinclair told BBC Sport.
“They have the experienced manager and the players at their disposal. They have a better squad than Norwich and come May they will be above the Canaries."
“The Black Cats' performances have been better than their results in recent weeks. I think they'll stay up,” added Lawrenson.
If the Black Cats are to stay up, they will need to find a way to get Jermain Defoe among the goals once again.
The striker has managed an impressive 15 goals in all competitions this season, 12 of which have come in the Premier League.
Recent weeks have seen his goal-scoring touch desert him though and that has seen his side seriously struggle to find the goals they need as a result.
If Sunderland can get him to add a few more to his tally between now and the end of the season however, their chances of staying up will be given a huge boost.