I beleive that you will need to use wildcards in your search portion of the ls statement.
As follows:
cd /
ls -la /*/* |awk '{ print $NF }' > /path/to/file # $NF will print the last field always so that you can get the filename intact with full path.
This will recursively list down 1 directory from the current directory. However, this will not do subsequent subdirectories. you will need to add a /* for each additional subdirectory and append that to the file you created with previous ls statements.
ls -la /* |awk ... > /path/to/file
ls -la /*/* | awk ... >> /path/to/file # append to first output.
ls -la /*/*/* | awk ... >> /path/to/file # and append again.
etc... ... ...
And the -a option will sort by alpha order as well. It will also pipe throught awk so that only the full path is listed and not file information.
There is another way but it does not show the full path.
ls -Rla |pg
This only shows a directory then the actual filename under that directory, not the full path as you requested.