To rub salt into Lions wounds, the 23-22 home defeat by Sale Sharks cost them leadership of Pool 3 and of the presence of hamstring victim O'Driscoll, likely to be out for at least a month.
"We have another chance - and this time we need to get it right," warned coach Gary Ella of their trip to the Sharks.
"We have to go to Sale and be positive, to play good rugby while being more patient. We were forcing things last Friday, going for it without the necessary build-up.
"The defeat was something of a combination of them playing well and us playing poorly - they attacked us from the start and we have never ever lost that amount of our own line-out ball in a single game. In the end we only played as well as they allowed us to play.
"But, make no mistake, Sale Sharks are a very good team and the guys who played in Dublin performed extremely well for their club. I thought our strength in depth in attack was pretty weak and that is something we will be working on.
"As to the loss of Brian, well, he is the best centre in the world by a long way and obviously any side would miss a player of his class. It is a big blow for us but we have to get on with the job of being without him for between four and six weeks."
Sale Sharks: J Robinson; M Cueto, C Mayor, G Bond, S Hanley; C Hodgson, B Redpath; K Yates, M Cairns, S Turner, D Schofield, I Fullarton, J White, A Sanderson (capt), C Jones
Replacements: J Roddam, B Stewart, C Day, M Lund, B Van Straaten, V Going, R Wigglesworth
Leinster Lions: G Dempsey; J Mcweeney, G D'Arcy, S Horgan, B Burke; C Warner, B O'Meara; R Corrigan (capt), S Byrne, P Coyle, M O'Kelly, B Gissing, E Miller, K Gleeson, V Costello
Replacements: E Bohan, G Hickie, D Dillon, A Mccullen, B O'Riordan, M Leek, D Quinlan
Referee: Rob Dickson (Scotland)