Both sides meet at the Stadium of Light on Saturday.
The Blues travel up North on something of a high after they ensured London rivals Tottenham Hotspur could not win the Premier League following Monday night's ill-tempered 2-2 draw at Stamford Bridge, in which Guus Hiddink's side recovered from a two-goal deficit.
In truth, the recenty-diposed Premier League champions have nothing but pride to play for in what has been a terrible season overall, but the Black Cats, on the other hand, remain in a scrap for their top-flight lives.
At the moment, Sam Allardyce's side sit one point behind 17th-placed Newcastle United - albeit with a game in hand, at home to Everton on Wednesday - and Lawrenson says avoiding defeat this weekend would tip the relegation battle in their favour somewhat.
He said to BBC Sport: "The important thing for Sunderland is not to lose on Saturday, because four points from their next two games would put them level on points with Newcastle - and probably put Sam Allardyce's side above them on goal difference with one game to play. 1-1."
The North-East side round off the campaign with a visit to Watford who, perhaps significantly for Sunderland, have little or nothing to play for, while Newcastle - who visit already-relegated Aston Villa on Saturday - host Spurs on the final day.