Easiest way to do this is have a background that's a "grid" (all your lines), and add it as the background image of your form; then, simply add buttons to the form in the designer and place them in each "cell" in your "grid".
At the end of the game, you can add pieces of each line as the background image to each affected button, as well as change the form background to the same line - it will look like a single line, but still allow the buttons to be clickable.
There's a way to do this programmatically as well, but a bit more difficult with buttons - look into Control.CreateGraphics()
method, to see how to draw with GDI+. More info here: https://learn.microsoft.com/en-us/dotnet/framework/winforms/advanced/how-to-create-graphics-objects-for-drawing