Can PS CC (or other programs) do that?
Crop - yes
Duplicate - yes
Flip - yes
Rotate - yes
All within a single edit file
Enlarge (resize) - yes
LR surely can do that too. These are simple manipulations, nothing fancy. How? I have no clue, I do not use LR.
PS CC, If I understanding what you did....
Create a document 2 and a half times original transparent background (250% the original size)
Import your document (let's say upper left for simplicity - I assume the original is ready to be worked on)
Place this import onto the upper left quadrant, in the center
Duplicate the layer. (Ctrl-J)
Flip the layer horizontally (mirror image right become left)
Move the layers content to the upper right quadrant
Select both layers.
Duplicate both layers (Ctrl-J)
Make sure the two new layers are selected.
Flip the layers vertically (top become bottom)
Move layers down so that they are aligned with the ones above
Crop the excess from the new document.
Resize
Done.
Note: Rotate is not used - Not needed (unless the original is not straight).
Then do whatever.
Caveats:
- A phone while offering a greater quality than before is not capable of producing images that can be really enlarged, even if the viewing distance is a factor.
- Cropping an already small original does not help the first issue.
- If you plan more modifications never save as JPG, JPG should be the last save, not an intermediary step.
As to originality of the image?