If I understand you in the right way, that you wish to block/cut the lines at a distance from the (letters of the) type, you may:
1) Lock/hide the artwork not to be affected;
2) Group the lines to be blocked;
3) Create a copy of the type below (above the lines) and lock the Original Type;
4) Type>Create Outlines, remove the inner parts of Compound Paths letters if desired for the right effect, and change fill to white for contrast; this is a group, called the Outlines Group below;
5) Object>Path>Offset Path to reach the desired block distance round (and inside) the letters;
6) Also select the Lines Group and Pathfinder Minus Front/Subtract from Shape Area.
Now you have the Original Type on top, the lines with blocked/cut out parts, and the artwork below.
You can move the type round to block different parts of the Lines Group by selecting the Original Type and the Outlines Group within the Compound Shape (Click and ShiftClick the rings to the right) and then ClickDrag.
Knockout group will getcha there.
Basically, it isolates transparency interactions to within the group. So a white stroke around the text set to multiply will not show up. So when knockout group is checked, the white stroke effectively punches through. Uh. Hard to explain, but easy to implement.
Group the text (with the stroke added via the appearance panel and moved below the fill to make sure not to nip out of the actual text.) and the line. Fully check "knockout group" in the transparency panel.
Thanks. This sounds like a solution. I'll give it a try.