The Red Devils managed to pull off a transfer coup after Manchester United signed Matic in a £40m deal from Premier League champions Chelsea earlier this month.
The Blues made the bizarre decision to sell to their direct title rivals despite the possibility of Matic transforming Manchester United into title challengers.
The Serbia international has already been named the club’s man of the match on two occasions this season and the 29-year-old helped to unburden Pogba.
The Manchester United record signing has scored two goals and has made one assist in his opening two Premier League games of the 2017-18 season.
Former Liverpool defender Lawrenson was quick to lavish praise on Matic for his impact on the Manchester United side.
“Romelu Lukaku has started well with a couple of goals but the signing of midfielder Nemanja Matic has just given Paul Pogba the freedom he needs,” Lawrenson told BBC Sport.
“Everybody knew he was a top player and that he just needed time. Well, I think the time is now.”
Pogba moved to Manchester United in a £89m deal from Serie A giants Juventus in the 2016 summer transfer window.
The France international was criticised for his underwhelming performances in his first season back at Old Trafford.
Pogba won four Serie A titles after the versatile midfielder moved to Serie A giants Juventus from Manchester United in 2012.
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