Last Saturday's dramatic win saw the successful return of Ireland internationals Kevin McLaughlin, Mike Ross, Cian Healy, Jamie Heaslip, Brian O'Driscoll, Eoin Reddan and out-half Jonathan Sexton who scored the match-winning drop goal.
Commenting on the Italian encounter, the province's head coach Joe Schmidt said: "The Treviso game was a real test - as we knew it would be. We were sluggish in the first half which could be a result of the hot weather conditions and the fact that we were integrating players back into the panel for the first time.
"But I was pleased that we managed to get the result. The players stuck to their task and ground out a good win against a combative and well-coached Treviso side.
"This week's test will be a big one because we saw last year, in their fine run to the semi-finals of the Heineken Cup, how good a side Edinburgh are becoming.
"And this year they seem to have improved further with greater strength in depth across the park. Tim Visser has six tries in just three games and Greg Laidlaw controls the game for them astutely.
"Having already recorded an away victory over the Cardiff Blues this year, they will travel to Dublin this weekend with confidence and we're well aware of their many threats. It'll be another big challenge for us and we'll need to be more co-ordinated than last weekend."
With Monday's field training session cancelled as a mark of respect for the late Nevin Spence, the Leinsteer panel will train on Tuesday morning and could be bolstered by the return of Gordon D'Arcy and reigning ERC European Player of the Year Rob Kearney, who are both in contention for the Edinburgh match.
"Of course preparations this week have been greatly affected by Nevin Spence's tragic passing," added Schmidt.
"Nevin was an extremely talented player and a hugely respected and popular young man within our squad, especially among all those players who played with him at underage representative levels and in the Ireland senior and Wolfhounds panels in recent years.
"The rugby, sporting and wider public have all been greatly affected by this tragedy. And it goes without saying that the thoughts and prayers of the squad - and everyone in Leinster Rugby - are with the Spence family and all of our friends in Ulster Rugby."
The Leinster v Edinburgh fixture marks the province's annual 'Kids Takeover' where younger supporters get the chance to be involved in the running of matchday.
Amongst lots of other events there will be 15 mascots leading the team out, a lucky supporter reading out the teams, the chance to make the presentation of the match ball and much more around the province.
Ticket sales have passed the 15,400 mark and are still on sale online here. They are also available from the Leinster Rugby Store (Donnybrook), Spar (Donnybrook) and Ticketmaster outlets nationwide.