False lines are used in leaded glass where the design calls for an angle that cannot be cut into the glass. This includes right angles and even more acute angles. E.g., the petals of a fuchsia flower. The design would call for an angle of about 60 degrees. This is impossible to achieve through cutting. So the glass is cut in a curve and the cames on the side and bottom of the petal have their hearts cut out so they overlap each other. The overlap is then trimmed to the shape of the outside of the petal. When soldered, the appearance is of the glass being cut at the angle required for the flower.
At other times, the requirement is for a line to go into a piece of glass, but not all the way across. Again you cut the heart out of the came, and overlay the smoothed lead onto the glass. You can use just a little silicone to hold the lead in place until you finish cementing. After this you can lift the piece of came and use silicone or epoxy resin to firmly attach the came to the glass. You do not want to do this before cementing as any excess of glue will be made dirty by the cementing process and be very difficult to clean up.
There are also times when you may want to have a silhouette, you can cut it out of lead foil and solder it into place. This allows intricate shapes to be made when a dark representation of the shape is required. If the panel can be seen from both sides, the overlays should also be on both sides. These should be glued to the glass just as for cames.
These principles can be applied to copper foil too.