The Warriors' last outing was the 38-21 six try rout away to Scarlets and Lineen is looking for much of the same from his charges.
"It was a fantastic result a fortnight ago," he said, "we scored some great tries, but we can't afford to dwell on that too much.
"We've got four big games left this season, two of which are at home, so it's vital that the crowd play their part and really get behind the players. Our target this season was to improve on our fifth place finish last year and we're so close to achieving that."
Utility back Colin Gregor retains his position at fullback having slotted four conversions at the Parc Y Scarlets to exceed 250 points in his six year career with The Biggest Team in Glasgow.
Meanwhile, centre Andrew Henderson makes the match 22 for the first time following the broken hand which he sustained during Glasgow's Heineken Cup win over Toulouse back in January.
MORE BIG NAMES HAVE SIGNED... NOW IT'S YOUR TURN.
Not only will Glasgow fans be able to back their team to the hilt as they go into battle with Ulster on Friday night, but they will also be first in line to sign for The Biggest Team in Glasgow and become a Warrior for the 2009/10 campaign as the new season ticket package goes on sale.
More big names have signed for next season. Thom Evans, Max Evans, Chris Cusiter and Rob Dewey will all be Warriors next season and now it's your turn.
The 2009/10 Glasgow Warriors season ticket has more benefits than ever before. On top of a match-by-match saving of over £100 (based on an adult season ticket), the new deal includes free entry for you and a friend for the pre-season friendly (opposition tbc), entry into the ticket ballot for RBS 6 Nations tickets, free admission to the away 1872 Cup match against Edinburgh in addition to two further Edinburgh fixtures at Murrayfield plus free entry into a Partick Thistle league game.
Season ticket holders aged 12 and under will also be entered into the exclusive prize draw to run out with the Warriors as the official mascot at a Glasgow home game.
Season ticket prices remain at just £30 for under 18s with concessions and students enjoying all the action for only £80. Adult season tickets are priced at £160.
Glasgow Warriors team to play Ulster in the Magners League at Firhill on Friday 17 April
15 Colin Gregor
14 Lome Fa'atau
13 Max Evans
12 Graeme Morrison
11 Thom Evans
10 Ruaridh Jackson
9 Mark McMillan
1 Kevin Tkachuk
2 Dougie Hall
3 Moray Low
4 Tim Barker
5 Alastair Kellock CAPTAIN
6 James Eddie
7 John Barclay
8 Kelly Brown
Substitutes
16 Fergus Thomson
17 Ed Kalman
18 Dan Turner
19 Calum Forrester
20 Dan Parks
21 Andrew Henderson
22 Bernardo Stortoni
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland