It may be a little late, but Hope is in sight
In Affinity Designer on my iPad pro i have no
Problem to do what you want
Set your (straight) Lines with the Pen Tool and then
pull/push it to a curve with the Node Tool.
This Gif was made with the Desktop Version of Designer
but works the same way also in Designer for Ipad.
Apart from the fact that Affinity Designer
does not have a couple of things that Illustrator has.
E.g. No perspective transformation and warping,
just one real vector brush, the other brushes are
bitmaps on a vector path. No Objects on a Path.
(Text on Path works)
It is still a powerful vector app ( for PC/Mac and iPad )
Has a includet Bitmap Studio Part. You can easly
paint ( also clipped) over Vectorforms with a bitmap brush.
For shades as an Example. A very cool Isometric Studio
and what i like mostly Symbols and Live Boolean.
You have more or less the same user interface on the PC/Mac
as on the Ipad, which I also like.
And for 22,- Euro on the iPad / 55,- Euro PC/Mac
I don't really see anything serious to complain about.