I've always been fascinated by the shape of SCORE's slurs/ties and I'd like to achieve this look in Lilypond.
My reasons aren't purely aesthetic.
Somebody created this code for me years ago but it has some major limitations. Maybe it can be useful as a starting point though. http://lilybin.com/67h327/1
As you can see, SCORE's slurs/ties aren't completely flat in the middle (the outer side isn't flat at all in many cases expect when the slur/tie is very long) and in fact you can specify how curved or flattened the shape is.
Here are some references to get an idea about the shape:
https://wiki.ccarh.org/images/c/c8/Score-Reference-Manual.pdf (printed pg. 51-63)
As requested by a comment I added a few images showing variations of the bezier curve.