Following is step by step for installing Lubuntu 12.04 on a 8GB flash drive on an Intel machine. Only the / partition is required.
Turn off and unplug the computer. (See note at bottom)
Remove the side from the case.
Unplug the power cable from the hard drive.
Plug the computer back in.
Insert the flash drive.
Insert the Live CD or Live USB.
Start the computer, the CD/USB should boot.
Select language
Select install Lubuntu.
Select Download updates while installing and Select Install this third-party software.
Continue
At "Installation type" select "Something else".
Continue
Confirm Device is correct.
Select "New Partition Table"
Click Continue on the drop down.
(Optional partition for use on Windows machine)
Click "Free space" and "Add".
Select "Primary".
Make "New partition size..." about 1000 megabytes.
Location = Beginning.
"Use as:" = "FAT32 file system".
And "Mount point" = /windows.
Select "OK"
Click "free space" and then "Add".
Select "Primary", "New partition size ..." = 4000 to 6000 megabytes, Beginning, Ext4, and Mount point = "/" then OK.
(Optional home partition)
Click "free space" and then "Add".
Select "Primary", "New partition size ..." = 1000 to 4000 megabytes, Beginning, Ext2, and Mount point = "/home" then OK.
(Optional swap space, allows hibernation)
Click "free space" and then "Add".
Select "Primary", "New partition size ..." = remaining space, (1000 to 2000 megabytes, or same size as RAM), Beginning and "Use as" = "swap area" then OK.
(Important)
Confirm "Device for boot loader installation" points to the USB drive. Default should be ok if HDD was unplugged.
Click "Install Now".
Select your location.
Continue.
Select Keyboard layout.
Continue.
Insert your name, username, password, computer name and select if you want to log in automatically or require a password.
Selecting "Encrypt my home folder" is a good option if you are worried about loosing your USB drive.
Select Continue.
Wait until install is complete.
Turn off computer and plug in the HDD.
Stick the side panel back on.
Note:
You may omit disabling the hard drive if, when partitioning you choose to install grub to the root of the usb drive you are installing Lubuntu to, (ie sdb not sdb1). Be cautious, many people have overwritten the HDD MBR.
You can revise grub later, if you wish.
Live USB
. There are tutorials on the net. Such as this one: ubuntuforums.org/showthread.php?t=1872303