Mid 2013 MacBook Pro displaying multi color
This could be one of two things:


a bad LCD
a failure of a logic board component, possibly the video mux chip.


A bad LCD is quite easy to diagnose; simply plug that LCD into a known working MacBook. If it continues to fail, it's the LCD.

Alternatively, you can plug in a known working LCD into your Mac and if it continues to fail, you've narrowed it down to your logic board.

If it so happens that your LCD tests good, the likely cause is the circuitry that sends display signals to the LCD itself.  


Cable
Video Mux chip
related circuitry (capacitors, resistors, traces, connectors, etc.)


What's a video mux?  It's a fancy switch.  It takes multiple inputs, in this case video,  and sends them to the appropriate output; the internal LCD and/or external TV/monitor.

That chip could be faulty given that it's only sending video to one display while sending garbage to another.  

Bottom line:  Take it in for service.

Swapping out LCD's is not too difficult, but you have to have either a spare LCD or a spare Mac with the same display connector.  I don't imagine you have spare Mac parts just casually laying around.

Doing a board level diagnostic isn't something you'll be able to do without the proper tools.

It can be fixed, but it needs to be done by a pro.