It does not seem there are many left-handed cursor themes. You have the following options:

comixcursors-lefthanded (ugly)

You have to install comixcursors-lefthanded and gcursor (gnome cursor theme managing software). Although gcursor doesn't seem to do install the theme for me it is useful to see what a cursor theme looks like.

The theme ComixCursors-LH-White-Small looks the most decent, so let's pick that one

Installation

First we need to add an extra line to the themes index.themes file. All themes are located in /usr/share/icons, and for the ComixCursors-LH-White-Small theme we need to do

sudo gedit /usr/share/icons/ComixCursors-LH-White-Small/index.theme

This file looks like this:

[Icon Theme]

Name = Comix Cursor LH White Small Bold

Comment = The left-handed Comix Cursors - White Small Bold

Example = default

Now we need to add the following line at the bottom (of course if you pick another theme, you should write the name of the other theme)

Inherits = ComixCursors-LH-White-Small

Now save and close the file.

On Ubuntu the utility update-alternatives manages the cursor themes, so we need to tell it about this new theme we want to use, execute

sudo update-alternatives --install /usr/share/icons/default/index.theme x-cursor-theme /usr/share/icons/ComixCursors-LH-White-Small/index.theme 91

sudo update-alternatives --set x-cursor-theme /usr/share/icons/ComixCursors-LH-White-Small/index.theme

Now if you log out and log in again, you should have your new cursors.

Note:

You can use

sudo update-alternatives --config x-cursor-theme

to change between the installed cursor themes.

Modifying the default (DMZ-White) theme (beautiful)

The above approach works but the cursors are ugly, however you can also modify the default theme. The cursors that you use most are the normal pointer and the hand (which appears if you hover over a link):

which are /usr/share/icons/DMZ-White/cursors/left_ptr and /usr/share/icons/DMZ-White/cursors/hand2.

The DMZ-White theme also provides a pointer that points to the right, and I made my own mirrored hand using gimp (see note at the end):

The pointer is /usr/share/icons/DMZ-White/cursors/right_ptr, and mirrored hand is called hand3 and I made it available on mediafire (if you follow the instructions below, you will download it automatically to the correct directory).

Now we need to replace these cursors. First go to the DMZ-White cursor directory

cd /usr/share/icons/DMZ-White/cursors/

Then download the hand3 cursor

sudo wget http://www.mediafire.com/download/v45c56ewol1k140/hand3

Now backup the original left_ptr and hand2 files

sudo mv left_ptr left_ptr_orig

sudo mv hand2 hand2_orig

Now let the new left_ptr and hand2 point to the right_ptr and hand3 files

sudo ln -s right_ptr left_ptr

sudo ln -s hand3 hand2

Now if you log out and log in again, you should have your new (beautiful) cursors.

Note: Editing cursor files using gimp

You can edit cursor files (and make your own cursor theme :) ) using gimp which is a free alternative to Photoshop. If you want to save your file choose Export to and then pick X11 Mouse Cursor. This will save your file with the .xmc extension, but you can simply remove the extension.