A Lions defeat at Eden Park on Saturday would consign the Lions to a 3-0 series whitewash, completing their worst set of Test results since 1983.
Cueto, who scored eight tries in eight England Tests last season but only gained Lions selection when Iain Balshaw withdrew injured, replaces his Sale Sharks team-mate Jason Robinson.
That is one of a handful of changes following last weekend's 48-18 defeat to the All Blacks in the second Test.
Wings Robinson and Shane Williams have been left out, with Lions head coach Clive Woodward switching Josh Lewsey from full-back to left wing and calling up Will Greenwood and Stephen Jones as respective replacements for injured duo Gavin Henson and Jonny Wilkinson.
Henson and Wilkinson are both suffering from so-called 'stingers' in their shoulder and neck areas, while a list of other players who could not be considered because of injuries include Charlie Hodgson, Ben Kay, Simon Shaw and Gordon D'Arcy.
Cueto and Irish full-back Geordan Murphy are handed their Lions Test debuts, and Cueto, for one, is determined to seize the moment.
"At the start of the international season, there was a 60-man England training squad named and I wasn't in that, but I managed to force my way in later on and I went on to play Test match rugby," he said.
"This is more of the same, really. I am just trying to do the things I know I am capable of, keep my head down and get on with it.
"Tuesday night against Auckland was almost my last chance, really.
"I put the Test match completely out of mind - I never really expected to be involved in it - and I sort of said to myself that Auckland was my last game of the season, let's give it a crack.
"You have just got to keep going. At the end of the day, you can moan and groan about selection, but the quality of player here speaks for itself, really.
"No-one can expect to be on that team-sheet, you've got to earn it and work for it.
"I think everyone knew they were going to get chances on the field, with the midweek games and everything, and it was a case of waiting and taking your chance.
"It is fantastic, the pinnacle of any rugby player's career, and it is no different for me. It is going to be a special occasion."
And Cueto wants the Lions backs to show their capabilities in a series so far dominated by New Zealand's attacking talent.
"A lot of credit must go to the All Blacks," he added. "They have been absolutely outstanding, and it has been brilliant to be able to watch them play such good rugby. From our point of view, I think we can learn a lot from them.
"But we've got the ability, we've got the talent out there - the game-breakers - in our backs to do the same. We've got to go out with the mentality we can do that, and we will do that.
"Generally, we've not got as much ball as we would have liked, but that is testament to how good the All Blacks have been.
"Hopefully, we can change things around this weekend, get a bit of decent ball and show what we can do."