When you open file manager you get

Now go to Menu --> Accessories --> File Manager --> right click, and choose properties

Change pcmafm to nautilus and you will get

However that only changes the application that will be opened by the shortcut "file manager". It does not make nautilus the "default file manager" in the proper sense: Opening a folder on the desktop, or opening a file location from an application would not open nautilus, but still pcmanfm.

Note: I will be adding information on how to make this change permanent in the next couple of days.

Note: This is my own personal opinion. I've tried these steps on my machine, and they worked. But I didn't like the outcome.

Change the contents of /etc/xdg/lxsession/LXDE/autostart as shown below.

From

@xscreensaver -no-splash

@setxkbmap -option grp:switch,grp:alt_shift_toggle,grp_led:scroll us,ar

@lxpanel --profile LXDE

@pcmanfm --desktop --profile LXDE 

@/usr/lib/policykit-1-gnome/polkit-gnome-authentication-agent-1

To

@xscreensaver -no-splash

@setxkbmap -option grp:switch,grp:alt_shift_toggle,grp_led:scroll us,ar

@lxpanel --profile LXDE

@/usr/bin/nautilus -n

@/usr/lib/policykit-1-gnome/polkit-gnome-authentication-agent-1

Also you can take a look at https://help.ubuntu.com/community/DefaultFileManager to see if it might help.

Edit:

In Ubuntu 14.04 here's what I did. I did a fresh installation of Ubuntu 14.04, and then installed LXDE. Once that was done, I set nautilus as a default file manager using the following command:

xdg-mime default nautilus.desktop inode/directory application/x-gnome-saved-search

and then I checked the current default file manager using the command below:

xdg-mime query default inode/directory

and it showed Nautilus as the default. See image below.