Hey, @Anna Claudia Speck. Welcome to the Lightroom Community. I'll help you figure this out.
You can create presets on Lightroom desktop & they'll sync over to Lightroom mobile. Head here to learn more: https://adobe.ly/4hIOm7H;
You can also create presets on Lightroom mobile; you won't have to paste presets manually into local folders. You can follow the guide here to import sample presets in Lightroom Mobile: https://adobe.ly/4hMfmmG;
Luts and presets are not available for Photoshop. However, you can interoperate between Lightroom and Photoshop on iOS.
Let me know how it goes.
Thanks!
Sameer K
(Type '@' and type my name to mention me when you reply)