But five years have passed since the last of their three titles and the younger brigade are as eager to bridge that gap.
For the more callow amongst them, an important stepping stone towards that goal can be laid on Friday evening when Montpellier come to Dublin. Win that, and Leinster will have wrapped up the pool with the chance of a home quarter-final to come.
It’s hard to exaggerate how big that would be for the new generation.
Of the 34 players the province has used in four European games this term, 20 of them have never played a knockout game of Heineken or Champions Cup rugby. Most of their number are guys who came up through the academy in the province.
Garry Ringrose spoke last week about the hurt felt by him and the rest of those greenhorns who made their Champions Cup bows last season when they slumped to five defeats in six pool games. This week, Tadhg Furlong, admitted that restitution must now be made.
“You have an obligation to the jersey and to make a commitment to it that you will perform as best you can and meet the standards of players that went before you. There’s a lot of us without any medals in our back pockets and you look at the senior guys with a lot of them.
“As a younger player you try to pay homage to what the lads have done but, in your own way, you want to move it on a bit as well.
“For lads to make European debuts last year, and then get knocked out in the pool stages with the tradition that the club has, it did hurt.
“It definitely feeds the desire for this year.”
Furlong and Ringrose were two of the half-dozen players pitched in for full European debuts this very week 12 months ago.
That fact, and the comfortable 25-11 win that day against Bath, were rare shafts of light to penetrate the gloom at the time.
It is, of course, an arbitrary point on which to judge progress made in the last year. Furlong isn’t long in pointing out that Leinster went on to top the Guinness PRO12 and reach the final and, though they lost the decider to Connacht, he took considerable worth from the experience.
His own story has gathered speed, too.
He was already knocking about Ireland camp last January and he points to his involvement in Ireland’s three-match summer tour to South Africa as a key staging post in his development as a tighthead prop of note.
That reputation was enhanced considerably in November when he impressed throughout the month and went viral for the snippet of action against New Zealand in Dublin when he shrugged off the attentions of two world players of the year.
The best part of it all is that he’s still only just turned 24. And, though he is keen to suggest that he is far from the finished article, he doesn’t pinpoint any particular areas of his game that are in major need of attention.
“I don’t think there has been a massive change in one big facet of the game,” he said. “It’s just a bit more experience, a bit more match fitness and starting a few more games. Last year there was a time when it was me, Marty (Moore, now at Wasps), and Mike Ross.
“You would nearly start one, sub one and rest one. When you have more involvement in match week, you feel that little bit sharper. That time in the saddle is massive and you get more at ease.”
Furlong sat out the October game against Montpellier at the Altrad Stadium when a physically imposing French side full of multinational talent turned the screw on Leinster up front, so this will be another new departure as he continues his education.
“It is a big test. They are a well-resourced, physical team. We know if we win we have a quarter-final place secured and we top the group. It is a huge test physically. It is a big game for the club, especially with how we went last year.”