Leinster have since lost just once in all competitions, with the Warriors one of only two teams to take points off them in the RaboDirect PRO12 this calendar year, courtesy of a 10-10 draw at Firhill back in February.
The Dubliners underlined their class in the Heineken Cup head-to-heads, inflicting a 38-13 defeat on the Warriors at the RDS before edging a tighter affair 23-16 in Glasgow.
Lineen believes it will take "something truly special from all 23 players" to see off a team who have booked another Heineken Cup final date for the following week, but has emphasised the belief underpinning his squad's approach.
The head coach told www.glasgowwarriors.org: "We've shown great consistency and character to reach the semi-finals, but this is where the hard work really begins.
"We're not satisfied just to be in the play-offs; we're absolutely determined to keep our run going, and that means finding a way to beat a side who are the benchmark for every other team in Europe.
"Leinster's record in both the RaboDirect PRO12 and Heineken Cup these past few years speaks for itself, and you only need to look at the statistics to see how hard it is to beat them.
"But we have confidence in ourselves, our game plan and each other and while we have huge respect for Leinster, we won't be standing back and admiring them.
"To win, we need every player to be better than they've ever been before. That's a big ask, but it's what it will take, and we've every confidence the players will deliver. They've risen to every challenge we've put in front of them this season, and this is undoubtedly the biggest yet."
The Warriors team for Saturday's match will be confirmed tomorrow morning. Lineen said: "Training has been excellent all week. As you would expect, the hunger and intensity have been right out of the top drawer, with everyone absolutely desperate to get into the 23 for the weekend.
"It promises to be another fantastic occasion, and the players will soak up the experience. But most of all they will be inspired by it and work to show the wider audience just how good a team they are."
Glasgow Warriors fans heading to Saturday's semi-final can take advantage of some great saver ferry packages offered in partnership with Stena Line.
For just £60 per person, supporters can travel from Glasgow city centre to Dublin via Belfast, with all coach and ferry transfers included.
The cost is just £199 for a car + four passengers on the Cairnryan to Belfast route, while great value ferry plus hotel packages are also available.
Please head to www.stenaline.co.uk/warriors for full information and to book.
We'll be running a fan zone for supporters in the Ballsbridge Hotel, just a 10 minute walk from the RDS. Full information will be provided on our official website, www.glasgowwarriors.org, and Twitter feed @glasgowwarriors later today.
For those unable to make the trip, we've arranged a special screening of BBC ALBA's live coverage at Waxy O'Connor's on West George Street.
Three big screens in the city centre bar will be showing the game, snacks will be available at half-time, and Warriors players will be in attendance to take in the action with you.
Under-18s can attend the screening, provide they are accompanied by an over-18.
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