Thin lines or tiny spots? Assuming somebody didn't draw perfectly straight lines on your screen with a very thin magic marker or apply dots with the same, these are symptoms of physical LCD failure. It's not liquid crystals themselves that fail, but the transistors that control their twist for individual pixels or address whole lines. The individual point failures may be tolerated if they aren't rapidly multiplying, it doesn't affect anything but your temper in terms of usability. Laptop manufacturers normally specify some smallish number of dead pixels after which they will change the LCD under warranty. The point pixel failure don't have to be dead black spots, they can fail "on" as well, meaning you'll always have a red, green or blue spot, which is more annoying than black on a white desktop.
A thick line, or a large black (dead) bar all the way across or up and down the screen usually indicates that the ribbon connector is partially worked of the LCD panel or the mainboard. This happens frequently on some laptop lemons where the connector was poorly designed and the cable is too short, so any vibrations or flexing of the case tend to work it loose. If it's not a loose connection, it's likely that the contacts on the display edge have separated, which means replacing the whole LCD unit.
