How can I make a persistent install of Lubuntu on my flash drive, so I can boot from my flash drive and save changes and files?
Running from USB is well supported by the standard Ubuntu setup, and there are a number of tutorials out there including this one.
In case that link vanishes, the procedure is as follows:
Installed to a USB drive that way, anything you save goes into the block of space reserved for such changes - this includes saving documents, installing new programs & updating existing ones, and changing settings - so the changes are available next time you boot using that USB drive. Not changes will be made to your existing drives unless you explicitly mount them using the new installation.
This should work equally well whether you are using a flash-based USB stick or an external drive connected via USB as long as your machine supports booting from such media.
I use this approach. It is quite useful, particularly when moving between different version of linux.
I have three usb hard drives, mainly for data storage, but I also use them for linux. I reserve about 50GB at the front of each drive. 45GB for the install and 5GB for the swap.
The Ubuntu installation to external drive since 9.04 has become simple. The only thing you have to be careful with is where linux puts GRUB. You'll want it on the external drive.
To make sure this happens, you have to select that drive in the last step of the pre-install questions. On this last screen there is an advanced button, click it and select the external drive from the list.