A wounded Spurs host the in-form Saints in the capital on Sunday.
Spurs welcome their South-Coast counterparts to North London on the back of a 2-2 draw at Chelsea, a result which confirmed Mauricio Pochettino's side would not be winning the Premier League and ending a 55-year wait for the title in the process.
Consequently, Lawrenson feels there'll be an "air of disappointment" surrounding the visit of the Saints, who are chasing Europa League qualification and appear to have hit form at just the right time.
Ronald Koeman's troops thrashed Manchester City 4-2 last weekend for what was their fifth victory in seven Premier League games, and Lawrenson says another positive result awaits them tomorrow, predicting a 1-1 draw.
"There will be an air of disappointment around White Hart Lane now their title hopes have gone," he told BBC Sport.
"If they were nowhere near the title then finishing second would be seen as a great achievement - which it is - but coming close means it hurts, and Spurs will be low.
"The circumstances will suit Southampton, though. They made the most of an atrocious display by Manchester City last week and have really found some form. 1-1."
Tottenham are without two key players through suspension, with Dele Alli serving the second of his three-match ban, while Mousa Dembele begins his six-match ban after being charged over the incident which saw him eye gouge Chelsea's Diego Costa in that heated night at Stamford Bridge.