I agree with hypnosifl's comment that they are referring to some or all of the pipeline/tunnel network.
Off the top of my head, the only times I recall this being roughly addressed in dialog are in The Matrix during the first sentinel encounter (right after Morpheus takes Neo through the city street training program where the woman in the red dress turns into Agent Smith), and the scenes in Revolutions where they're talking about how to get back to Zion.
The Matrix (note that this dialog isn't in the shooting script):
Neo: Where are we?
Trinity (whispering): They're old service and waste systems.
Neo: Sewers.
Trinity: There used to be cities that spread hundreds of miles. Now these sewers are all that's left of them.
Revolutions (I couldn't find a clip of this so I'm quoting a script; may not be exact):
Niobe: No it’s not. There’s another way. A support line. It drops down right here. A thousand meters short of 21. If we’re lucky, we may be able to slip down without them ever knowing.
Roland: That’s a mechanical line. It’s impossible, no one can pilot mechanical.
Combined I think those are reasonable support for interpreting "lines" as shorthand for tunnels/pipelines.
The shooting script for The Matrix also refers to waste lines, sewer mains, supply lines, and pipes. For example, here's how the shooting script describes where they park the ship right before the dialog I quoted above from the Sentinel scene:
Morpheus scans the decayed landscape of the sewer main that rolls by as Neo and Trinity squeeze into the cockpit behind him. An alarm begins to sound.
... omitted dialog ...
Neo feels the ship rock to the side as it squeezes into a tiny supply line.
The Nebuchadnezzar sets down, almost wedged into a pipe that barely accommodates its size.