Alli joined Tottenham from MK Dons in February 2015 for a paltry fee of £5million before being loaned back to the League One outfit.
The midfielder returned to White Hart Lane ahead of the 2015/16 season and immediately established himself as a key member of Mauricio Pochettino's side.
Alli won the PFA Young Player of the Year award at the end of his breakthrough season in England's top tier and is on course to retain the accolade this term, having excelled again to help Spurs climb to second place in the table.
Liverpool showed an interest in Alli before Spurs had even made initial contact with the youngster and Larwenson is adamant the pain of failing to secure the services of a such huge talent is still being felt at Anfield.
Lawrenson told you-are-the-ref.com: “He was going to Liverpool. It was absolutely all done and sorted but Liverpool had a change of heart the next day.
"It was a change a heart over money rather than the actual boy. They are regretting it every single minute of every single day.
"He’s a player isn’t he, as in he’s one of those lucky lads who can be anything that he wants to be but he also has that little bit of edge about him.”
Dele Alli has scored 16 Premier League goals this season; more than any individual total managed by a Liverpool player.
The midfielder, who turns 21 today, signed a new long-term deal at White Hart Lane worth nearly £55,000-a-week in September 2016.
But Lawrenson has claimed not everyone within the Spurs hierarchy was immediately sold on the youngster's potential: “The other thing as well is Tottenham have a transfer committee and I know one of the guys on it .
"When they went to buy him only three of the five said yes. When I say only of course only three was enough.
"I saw him at Preston a few times against MK Dons and he pretty much just ran the game,” Lawrenson added.
Spurs boss Mauricio Pochettino has described Alli as 'a son' and believes the midfielder is the best young player in Europe.