Say I have Ubuntu installed in a hard drive
What can I do to generate a liveUSB that is as similar as possible to the installation ?
I recommend using Remastersys.
This will create a hardware-independent LiveCD ISO backup of your system; you can then use a tool such as Unetbootin to "burn" the ISO to a USB and create a LiveUSB.
Remastersys includes both command-line and GUI front-ends. Note that the author recommends starting with a "clean" install and then customizing it to maintain the highest compatibility for the LiveCD/LiveUSB. There is also a 4GB final size limitation, which means that your Ubuntu install should be around 8GB at most, and you should not include any media files, deb files, etc.