The Glasgow coach has had to work overtime this week to refocus the minds of players after a turbulant week in Scottish rugby.
As if that was not enough to worry about, Glasgow's opponents in tomorrow's European Challenge Cup quarter-final are Saracens, who have lost just once in the Guinness Premiership since 1 January. A resounding 36-5 defeat of Bristol at Vicarage Road last weekend has moved them into third in the table.
Both teams have the attraction of a home semi-final, against either Bath or Bristol, and Lineen knows that his side's improvement this term would take on a whole new glow were they to stun Saracens on their home patch.
He said in The Scotsman: "Obviously, the guys read the papers and it's been a pretty big week, but hopefully we're professional enough just to get on with the game. Alastair [Kellock] sat the boys down after the SRU meeting on Tuesday and talked about it and got it out of the way and we said 'our focus is this game against Saracens; it's going to be fantastic, let's enjoy it and not take anything away from what we've created here'.
"This is massive for these guys, for Glasgow and Scottish rugby. The players have created this opportunity and deserve to be here; now it's up to them to do themselves justice on Sunday against what is an outstanding Saracens outfit. I know them pretty well having watched their games and know the outstanding talent they have.
"We know it will be tough - they're on a good run at the moment, but we're had a good few wins ourselves and there is a lot of belief in this squad; our players are buzzing. This is a one-off and though this isn't the end of the season - we have Leinster the following Friday - but everything right now is about this one game.
"They have to go out there and leave nothing behind; that's important. We have some quality players who will be on the biggest stage they've ever been on and it's up to them to go out in European competition, playing with their mates, trusting each other, and enjoying it, and giving everything they've got for Glasgow.
"Make no mistake, we're going down there to win. We're not going down there to hold them to however many points; professional sport is all about winning. The incentive of a home semi-final is absolutely huge."