However, before the Irish side embarked on this terrific run, Glasgow did record a 23-19 success over their semi-final opposition and also held them to a 10-10 draw in February.
And it is these previous success stories that gives Lineen the belief that they can reach the RaboDirect PRO12 final.
"We've shown great consistency and character to reach the semi-finals, but this is where the hard work really begins," Lineed told the Warriors website.
"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."
63x46.png){kind=logo}