A bit mixed up on those lpe-s.
You made a group of four paths, and applied bend and pattern along path lpe on them -haven1t thought of it would be possible.
Patten along path extesion works with paths but not the lpe, as per se.
So the gradient you want to be bent is a linear one, in a random direction to the axis.
If the path bends at an even radius, a parallel gradient would turn to a conical one.
A perpendicular would turn to a radial gradient.
At any angle in between it would need to turn each of the colour steps to a logarithmic spiral shape.
Knowing the core path would hardly bend at an even radius, there would be other large distortions needed.
Svg only supports linear and radial gradients.
If duplicating/cloning the pattern and transforming manually is a no-go, and you want a really bent look, you need some other solution.
For example draw a shape more detailed than the output pixel grid, representing the gradient with flat colours, and bend that instead.
-by meaning bend, draw the core path and add a pattern along path lpe to it, then set the pattern.
https://openclipart.org/detail/202509/blue-ouroboros-by-lazur-urh-202509