The 27-year-old Honduras left-back was signed from Motagua in his homeland in the wake of his displays at the World Cup in South Africa four years ago and has developed into an integral part of the Hoops' side.
After Celtic clinched their third successive title with a 5-1 win over Partick Thistle at Firhill on Wednesday night, Lennon turned his attention to next season and what he will have to do to replenish his squad.
The Northern Irishman admitted that "it is looking more and more likely" that Greece forward Georgios Samaras, who is out of contract at the end of the season "will be playing his football elsewhere," and there is speculation about the future of Dutch defender Virgil van Dijk and keeper Fraser Forster.
However, Lennon knows where he might find replacements.
Ahead of the visit of Ross County on Saturday, he said: "We watched Emilio at the World Cup in 2010, particularly against Spain and he played very well against Navas.
"Obviously we decided to take him in and he has proved to be a very good buy for us.
"So there is no question that the World Cup may come to our advantage but I am sure 100 per cent of all the managers will be saying the same thing.
"I would like to go. The last one I went to, France 1998, the opening game of the World Cup was between Scotland and Brazil, so even though it is the other side of the world I may look at the opportunity of going at some stage to do some scouting."
The former Celtic skipper is aware that his side's championship win, in the absence of traditional rivals Rangers who are making their way up through the leagues after falling into administration and liquidation, did not elicit widespread praise, particularly from south of the border.
However, Lennon used an Andy Murray analogy to insist the Parkhead club's achievement should not be talked down.
"Probably the overview isn't great because Rangers aren't here," he said.
"That is a realism and there is nothing we can do about that.
"But I don't like the word devalued or anything like that.
"When Andy Murray won Wimbledon there was no Rafael Nadal so does that mean his Wimbledon title is devalued because the best player in the world wasn't at it? No, it doesn't.
"Nor should it mean the same with the titles we win.
"I think because we are the dominant team that what is overlooked is that we have some very good players here.
"And every season throws up different challenges.
"This year we sold some very good players and it was a challenge to replace them and I have not finished trying to do that.
"But some of the players who have come in have definitely improved, particularly the second-half of the season."
Lennon confirmed that he will rest some of his top players in the final seven games of the season, with more than a nod to Izaguirre and Nigeria defender Efe Ambrose who will definitely be in Brazil, while Forster is hoping to find a place in Roy Hodgson's England squad.
He said: "We are back in on the 24th of June and we will have everyone back apart from those at the World Cup.
"So I would like to give some players a break, particularly the ones going to Brazil.
"We used the opportunity last year, where four had a break then another four had a break.
"But my priority is to give the players going to the World Cup to get a rest because we have been going at it basically for two years so this is the first chance to give them a proper holiday."
Looking forward to the visit of the Staggies, Lennon said: "I would like to keep our consistency going because we are actually playing very well.
"I am really pleased with the way we are playing an expansive brand of football at the moment."