Average speed cameras were installed on the busy two-mile stretch of road after a campaign by residents and councillors to tackle dangerous driving.
In a series of court hearings held behind closed doors last month, Lamela and Vertonghen, as well as ex-Spurs star Jermain Defoe, 38, were all fined and handed penalty points on their licences. Dier was given a six-month driving ban starting on December 8 after he admitted a single speeding offence.
In April last year temporary speed cameras were set up on the A10 between Bullsmoor Lane and Southbury Road, where the limit is 40mph. Transport for London reported in June that 14,774 fixed penalty notices had been issued in the first months of the cameras being in operation.
Premiership players began returning to training in small groups on May 19, two months after the country was plunged into lockdown because of the coronavirus pandemic.
Lamela admitted being caught out twice when he was clocked at 52mph on May 8 and 48mph on May 13, landing him with six penalty points, £720 in fines and costs and fees of £264. A third speeding charge against him, allegedly committed on May 20, has not yet been dealt with by the court.
Dier was handed a driving ban on December 8 for speeding at 49mph in his Land Rover on May 20. He pleaded guilty and was also ordered to pay £270 in fines and costs.
Vertonghen, who left Spurs this summer for Benfica, was caught out by the speed trap on May 25 when he was driving at 48mph, landing him with three points on his licence, a £220 fine plus £124 in costs and court fees.
Defoe, who now plays for Rangers, was fined £600 and given six penalty points plus £156 in costs and fees for not responding to a notice of intended prosecution. His Land Rover was caught speeding on May 18 at 61mph but he did not write back to the authorities to say who was driving.
He also faces an allegation of speeding the next day but that case has been put back to January 27.
Representatives for Dier, Vertonghen, Lamela and Defoe have all been contacted for comment.