Lampard's side gave their bid for Premier League safety a huge boost by recording a 1-0 victory at home to third-placed Chelsea in Sunday's clash at Goodison Park that has left fourth-bottom United's destiny out of their own hands.
Leeds remain two points clear of the drop zone which is still headed by third-bottom Everton but the Toffees have five games left on their agenda as opposed to the Whites who have just four games to go.
The Whites are level on points with fifth-bottom Burnley on the same amount of games played but the Clarets have a far superior goal difference in their own bid to avoid the drop.
Everton, meanwhile, have now taken seven points from their last four games but Lampard has highlighted the number of points still available to play for and the need for his Toffees to address their terrible away form between now and the end of the campaign.
Everton have taken just six points on their travels all season with 16 games yielding 12 defeats, three draws and just one victory and trips to Leicester City, Watford and finally Arsenal are still in the offing.
Home games against Brentford and Crystal Palace complete their run-in.
“There are a lot of points to fight for," said Lampard, as quoted by evertonfc.com"We are still in the relegation zone, we have the extra game but we have to go with that same spirit in every match.
“I prodded the players a bit before today’s game, because I thought they needed it.
“The situation is clear, we need to perform at that level in our remaining games.
“They did what they’ve done at Goodison for me, performed with spirit and togetherness and tactical organisation.
“This is not the time to enjoy it and relax. There is a reason we are where we are and a big part of that is the away form.
“People are right to ask questions if the players don’t produce that level of performance against Leicester and Watford.
"It is a different demand from now because it is critical – it is no good waiting until there are two games remaining, we have five games and are in a fight and it is in our hands to perform how we did today."