However with Ulster and Scarlets breathing down their necks the Warriors can afford nothing less than victory.
The form book suggests that this will be delivered, Glasgow only losing two of their last 16 RaboDirect PRO12 games.
However, Treviso were the last side to beat the Warriors at Firhill, winning 15-13 there last September, and it is with this in mind that Lineen is urging his troops to stay vigilant with a lot at stake from their Italian adventure.
"For a while now, the next game has been our biggest of the season, and that's certainly the case again this weekend," Lineen told the club's website.
"We know we have to win this match if we're going to make the play-offs, and there's absolute clarity and focus among the players about what we need to achieve and how we're going to do it.
"Treviso is right up there with the toughest places you can go in the RaboDirect PRO12. They're a passionate team with supporters to match, and some of the results they've recorded this season speak for themselves.
"The wins we've managed on the road this season at places like Leinster, Cardiff, Ospreys and Aironi have been brought about by 23 players performing right at the top of their game. That's the recipe again this weekend, and we're certainly going to have to be much better collectively than was the case in Munster.
"We didn't get into that game anywhere near quickly enough, and we paid for it in the tries and penalties we conceded. The second half performance was much more like the real Glasgow Warriors, but we still need to see an improvement in terms of discipline and composure.
"We've seen a good number of times this season that the players know what it takes to deliver when the pressure is on, and we've every confidence they will back up all that good work with another winning performance come Sunday."
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