The easiest way to install Lubuntu on any USB pendrive is to boot your Lubuntu Live CD/DVD, enter the live session, and use the Installer icon present on the desktop. Make sure first that your Internet connection is up and running.
After you get to the window with the 3 options for installing Ubuntu/Lubuntu, choose the 3rd one which says Something else. This way you'll be able to access the partition table for both your hard disk and the USB pendrive. Choose the medium where you want to install Lubuntu, which of course has to be the USB device, and after that delete your entire USB partition if you haven't done it already.
Next you should create 2 new partitions on the USB pendrive: the first one will be the root partition formatted as linux ext4 with foreslash / as startup or mounting point, and the second one has to be a small Linux swap partition (around 1-2 GB in size). After you are finished with partitioning the USB select the root partition and press NEXT to start installing Lubuntu on the USB pendrive. DO not leave any free space on your pendrive, be it raw free space or fat32 formatted free space!!!
Most important thing is to choose to install the bootloader on your USB and not on your HDD device. While still facing the partition table for your USB, select from the drop-down menu at the bottom of window to place bootloader on the USB pendrive. Make sure you select the entire USB and not your new root partition for installing the bootloader / grub. This way your new bootable Lubuntu usb pendrive will be 'completely independent of it's host'.
I strongly recommend you download and burn on a CD/DVD Lubuntu 12.04.4 LTS iso image or Lubuntu 13.10 because lots of users have experienced nasty errors when trying to install this new Ubuntu 14.04 and all its derivatives, Lubuntu 14.04 included.
On a last note, to be able to boot from USB you have to either change your BIOS settings to do so or you can just press your default BIOS key for the boot menu (which is usually F12) and select to boot from the USB pendrive. I prefer to press F12 to get to the boot menu because I find it more convenient for me.