If you are getting the same problem on an external monitor then the problem cannot be your LCD panel despite my having said that.
First make sure that the external monitor you used is free from such lines when used by other PCs.
If the external monitor exhibits lines on other PCs then use a different monitor to test.
If however the external monitor is good then that would suggest a more serious problem with your laptops graphics.
If it is your laptop graphics then the options you have depend on the type of graphics used in your laptop.
There are essentially two different types of graphics processors that can be found in computers in general: integrated and dedicated. For laptops it is more common (for cost, battery power and heat reasons) for it to be integrated. There are exceptions but that is usually found on more expensive higher end laptops.
If your laptop has integrated graphics then you would need to replace the motherboard.
If on the other hand it has a separate dedicated graphics module then that could be replaced so long as you can find the replacement part.
You would need to consult your laptop documentation and manuals to see what you have.
Replacing laptop parts (whether it is the LCD panel or graphics module or anything else) is not simple. You need the right tools, a good manual showing how to dis-assemble and assemble your laptop and a lot of patience.
Laptop parts are often sold by second hand dealers on ebay who cannibalise broken laptops and sell on their working parts for spares. The more popular your laptop the more likely you will be able to get a spare for it.
LCD screens tend to be sold either with the complete housing or sometimes just the panel itself. Each requires a different approach to replacing the part.
Similarly you could buy graphics modules on ebay. However, different laptops have different types and therefore you would have to ensure that you get one that will fit in your laptop.
Sometimes you can even buy faulty laptops of the same model as your laptop on ebay which may also be another way to source parts.
There is always the more expensive route of going to your laptop manufacturer who will probably have the part/s available at a price especially if it is a more recent laptop. Older laptops may not be supported by them anymore though in which case ebay is the most likely option.
As you can see from my response you need to do a bit more research into what exactly is the problem before you rush off and buy parts that you might not need.
I hope it helps.
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☺ When everything else fails, read the instructions.
