The former England international was Lampard’s first choice as a substitute just before the hour as he chased the game but it was not until the second minute of additional time that Alli made his mark.
Chasing down a ball into the corner he retrieved possession and his cross led to Richarlison scoring, which moved them four points ahead of 18th-placed Burnley ahead of their home game against Southampton on Thursday.
It was only Alli’s seventh appearance – all as substitute – since his deadline-day move from Tottenham but Lampard hopes it could be the spark which helps him regain his form.
“We needed a goal and he has trained well,” said the manager when asked about his choice of substitution.
“It is not easy to demand from players who are not playing so much to come in and have an impact but you have to train well to show your manager you deserve a chance and he has done that.
“Clearly he has done that in training, and then you get your bit of luck or something happens for you and that happened with Dele.
“He deserves it; he ran into the corner, he bullies someone and gets the ball back into the box and we score off it.
“I was really pleased with that part of it from him and hopefully that can be a big starting point for him.”
Lampard admits the transition to a new club – and one that was struggling – after seven years at Tottenham was always going to be tough for the 26-year-old.
“I don’t think the story was ever going to be simple with Dele; we know the situation he came to us in terms of how the last couple of seasons have looked and the high level he reached for a big period of time at Tottenham.
“Sometimes you have to work and fight through things and we are in that process with him.
“I have a big level of communication with him and I explain a lot to him in terms of the demands of training and application and being ready for whenever that moment comes.”
A point was more beneficial to Everton than it was to Leicester, who remain in ninth and 11 points adrift of likely European qualification.
Additional reporting from PA