The Reds were 4-3 winners in a scintillating game at Anfield.
The Reds hosted the German side in the second leg of their Europa League quarterfinal tie a Anfield on Thursday.
It proved to be a remarkable evening as they battle back from 2-0 down, then 3-1 down, to win the game 4-3 with a later header from Dejan Lovren.
After the 1-1 draw in the first leg, that saw them through to their latest European semi final in another special night at Anfield.
It is not the first time they have fought back in that manner, but Lawrenson says this occasion was the comeback of all comebacks.
"An amazing, amazing game! That will live long in the memory. It is the comebacks of all comebacks,” he told BBC Sport.
"For Liverpool to get themselves back in this game, let alone win it, is a fantastic achievement."
"Just the sheer bloody-mindedness and determination of the Liverpool players who played tonight has been absolutely magnificent."
Jurgen Klopp’s side will definitely feel they can go on and win the tournament after this impressive victory.
Dortmund were among the favourites for the competition, but Liverpool have managed to see them off, potentially putting them at the top of the pile here on in.
And with a Champions League place up for grabs for the winners, they will certainly be keen to go on and win it with a top four place looking out of reach.