And now Lineen has demanded that his side round off their group efforts with another victory against Newport Gwent at Firhill, the Dragons having won in Glasgow two weeks ago in the Celtic League.
Scotland stars Kelly Brown, Dougie Hall, Alastair Kellock, Max Evans, Thom Evans, Ruaridh Jackson, Graeme Morrison and Dan Parks - who were all this week named in the 33-man pool for RBS 6 Nations opener against Wales - are all in the Warriors squad for the match.
Lineen said: "Last weekend's game was a fantastic result for the club and I'm proud of the way the players responded to the call for a big performance, both from themselves and the fans.
"It was a very physical game which saw us lose another few guys through injury so that's been a challenge this week as we look ahead to the visit of the Dragons.
"Our record against the Dragons is frustrating and something we really need to put right. The passion and aggression of the players was evident last week and we must carry that into this Sunday's game if we're to get the result we are all looking for."