I found a way to make it work, tough. Certainly, it's not the most elegant way, since I have no idea how to create a Libreoffice extension from source.

You can download the modified extension for 32bit here: lo-menubar.oxt
Download it, open it, agree in Libreoffice to install it, restart Libreoffice.

I hope I didn't violate any licenses…

If you don't trust me or your just curious what I did, here is what I did:

Download the extension that was mentioned in the other answers:
lo-menubar.oxt

Get the 32bit deb from the Ubuntu repositories. Open a terminal and enter:

apt-get download lo-menubar

If you didn't change the directory, a file called *lo-menubar_0.1.0-0ubuntu1_i386.deb* should be in your home folder.

Now open lo-menubar.oxt with the archive manager: Right click on the lo-menubar.oxt, open with archive manager (I hope it's called like that, I am using Ubuntu in German)

Now both files should be open, each in an archive manager window.

In lo-menubar.oxt:

Remove the Linux_x86_64 folder

Change into the folder META-INF

Extract manifest.xml (just drag it onto your desktop)

Right click on the extracted manifest.xml - open it with a text editor

Find *platform=Linux_x86_64"* and change it into *platform=Linux_x86"*

Find *Linux_x86_64/menubar.uno.so"* and change it into *Linux_x86/menubar.uno.so"*

Save the manifest.xml and close your text editor

Drag the manifest.xml back into the archive manager, which has lo-menubar.oxt opened, to overwrite that file

Go back to the root folder of lo-menubar.oxt, keep it open.

Open the lo-menubar_0.1.0-0ubuntu1_i386.deb with the archive manager: Right click on lo-menubar_0.1.0-0ubuntu1_i386.deb, open with archive manager

Change into the folder: /usr/lib/libreoffice/share/extensions/menubar/

Drag the Linux_x86 folder into the lo-menubar.oxt

Close everything and open the lo-menubar.oxt. Restart Libreoffice.