With just five games remaining, Glasgow remain in fourth place but it promises to be a nailbiting run-in with three teams within two points of snatching that final play-off place.
And despite the news of Lineen's departure to a post within the SRU taking most supporters by surprise, the New Zealander is adamant all that matters is securing a top-four finish.
"You'll have read and heard about the new position I'll be taking on within Scottish Rugby at the end of the current campaign," Lineen wrote in an email to the club's supporters.
"As I said last week, the role excites me and, while the timing of the announcement wasn't ideal from anyone's perspective, you have my word that the focus of everyone at the club remains firmly on the task in hand: reaching the play-offs.
"Two words sum up the mood at the club right now: excitement and determination. With five games left in the regular season, we're in the semi-finals places, and we'll be doing everything in our power to ensure we're still there come full time against Connacht on May 5.
"The players and staff have worked incredibly hard to put us in a position to kick on and achieve a top-four place for the second time in three seasons. And it's now about making sure we finish the job by sticking to the principles that have got us to this point: hard work, team spirit and absolute commitment to the cause.
"As the players' own motto goes - 'whatever it takes.' "You the supporters have a great opportunity to throw your weight behind the play-off push in the next two games, both at Firhill, against Aironi this Friday and Cardiff Blues the following Friday."