A Lions side consisting of Tim Cahill and Kevin Muscat got through to the 2004 decider - only to be beaten 3-0 by Manchester United - and Lowry is looking to at least equal that as the South London club prepares to take on Championship rivals Blackburn Rovers in the quarter-finals on Sunday.
"Playing Blackburn at home is a massive opportunity for us to get to the semis - and if you do that then anything is possible.
"It's the dream of most players to play at Wembley in a final and the FA Cup is one of the big ones. I've never played there and it's great to be in with a chance this season.
"It would be incredible to go all the way with Millwall. I certainly fancy us to reach the semis because we have home advantage against a team from our own division - and that's a huge plus."