Warriors gave Saracens a major scare in the European Challenge Cup last weekend.
And the Scots believe they are a stronger side than their current ninth place in the Magners League suggests, and are determined to prove it at Hughenden.
With Warriors the only pro team to benefit from Scottish Rugby Union direct funding next season, the pressure is on the Glasgow side to ratchet up their level of performance and improve results.
Lineen said: "We've got a point to prove this week and we want to continue the form from our game against Saracens, particularly from the second half last Sunday.
"We haven't beaten Leinster in a while and both teams are now fully focused on the Magners League.
"We've got five games left of our season and a lot to prove. We're hoping for a good crowd as it'll be a great night for fast running rugby."
Other than Barrow coming in for Henderson, Glasgow are unchanged from the side who lost 23-19 to Saracens.