According to this source the definition if Permute Lines submenu is following:
{
"caption": "Permute Lines",
"children": [...]
}
And it doesn't contain an id. Is there a way to add items to this submenu?
Also this source is 5 years old and is probably for Sublime Text 2. Is there a more recent version of default menu file?
To answer your second question first, you can always get at the most recent menu definition from your own copy of Sublime; it's stored in the file Default\Main.sublime-menu, which you can get to most easily using PackageResourceViewer to open it up.
That said, the part of the menu that you're referencing in your question is the same between Sublime Text 2 and Sublime Text 3 and neither of them has an id value directly within the Permute Lines sub-menu.
By creating a Main.sublime-menu in some other package (e.g. your User package) you could create entries that are adjacent to that sub menu, but in order to actually put new content directly inside of it you would need to create an Override.
You can do that via PackageResourceViewer; if you use it to open up the Default\Main.sublime-menu file, you can modify the file and when you save it, it will be saved as an override.
From this point forward your override becomes the new default menu; other packages that extend the menu can still do so, but they will be merged with your version and not the shipped version.
This is not without its risks in that if a future version of Sublime Text includes a modified version of the menu, your override will still take precedence and you won't be warned that it's happening, so you could potentially miss out on fixes.
This happened recently when the latest build of Sublime modified the base menu to include an install link for PackageControl, for example.
Also, this is only a viable solution if you want to edit the menu for your own purposes; if you're a package author, you can't use this method to distribute your own changes.