Cockburn saw his men deliver the Scottish Hydro Shield with a battling victory over league champions Greenock Wanderers. Lasswade now require eight points from their matches at home to Newton Stewart and Hawick YM to join Wanderers in stepping up to Division One.
The coach has left his players in no doubt that, while the knockout glory was a significant achievement, it is very much a secondary issue.
"I would swap it for being second in the league," he said "The key point is getting up the leagues and getting into Premier Three. That's what it's all about."
Results over recent weeks have made the task slightly easier for Cockburn's men as he acknowledged, saying: "When we looked at the last five weeks we had to get three five pointers and two four pointers. We've got the five pointers so we don't have to worry about bonus points which takes the pressure off."
At present, Lasswade sit third in the table, eight points adrift of Glasgow Accies, who have concluded their campaign, but with a superior points difference. While Saturday's visitors have struggled this season, Cockburn is confident that his players will not underestimate the scale of the task they face. "This level of rugby is very competitive, sometimes a wee bit coarse but they have a lot of skills."
Lasswade go into the match with confidence high after last weekend's win and Cockburn will happily settle for two repeats of that performance to round off a lengthy campaign that has seen him seek outside assistance to ensure his men remain motivated.
"Technically, pre-season could start in eight weeks," he pointed out. "In the last five weeks we have been working hard on trying to manage the training. It's been ten months. I've been trying to get other coaches to come in just to get a different voice and freshen things up."
He is confident his men will approach the game in the correct manner, although there are no such guarantees on post match activities.
"The guys enjoy themselves every Saturday. They have a real professional attitude, they use the ice bath, we weigh ourselves and rehydrate afterwards but it becomes a bit more old fashioned later on," he concluded.