The Steelmen, should they progress past Aberdeen a week today, will face a trip east to high-flying Hibernian, who knocked out cup holders Hearts on Sunday.
Stuart McCall's side came within seconds of qualifying for the fifth round until Niall McGinn popped up to cancel out Jamie Murphy's long-range strike at Pittodrie.
But while Lasley is less than pleased at a possible match-up with Pat Fenlon's Easter Road side, the Well skipper believes his team can take confidence in the game being away from Fir Park, with Motherwell only having lost two games away from home all season out of a possible nine.
He said: "You would have to say that the draw has not been kind and I don't think either Aberdeen or ourselves would have been desperate to land a trip to Hibs.
"I watched their victory over Hearts and they have developed an ability to win games even when they've not played well.
"On top of that Easter Road seems to be a place with a real buzz about it and Hibs have a fantastic support who really get behind them.
"Whoever prevails between ourselves and Aberdeen will have to be at their best for the trip to Leith. I would say that outside of going to Celtic it is the toughest draw we could have landed.
"But, on the other hand, if we can get past Aberdeen in the replay next Tuesday, our away form has been very solid. So that would be a positive."
McGinn's leveller for the Dons was a case of deja vu for Well after the former Celtic ace netted back in September to help rescue a point for the home side in a thrilling 3-3 draw.
Lasley admitted: "To lose the equaliser so late was very hard to take.
"It was a similar story in our league game up there but I think, although it was hard to do at the time, you have to look at the positives.
"We went up to Pittodrie and weathered a real storm as Aberdeen started really well and then got a great goal from Jamie Murphy. We were really pretty comfortable.
"So it is up to us to repeat that level of performance and make sure that we make the most of home advantage in the replay."
The Dons replay will be Well's second home game on the bounce with Saturday's SPL encounter with Ross County first up, and Lasley has no doubt about the importance of returning to winning ways on home soil.
The Well captain said: "To only have the one win from eight home games is just not good enough and it is a frustration for us.
"But we have put together an unbeaten four-game run and we will go into the County game with renewed determination to get three points at our place."