I have a vibrato function that is highly parameterized. If the picture here gives you some idea, I can post the code. Using the right arguments you can achieve pretty close to what you have. And you can rotate objects easily, as per your picture.
An alternative is to code the oscillating path in PostScript, which lilypond supports just fine (but then you can't output it to SVG, in case that is an issue.)
But no, this sort of graphical gesture is not available in lilypond as a built in. But lilypond can be made to do anything.