Response to edited question
Edit: Is there a way to tell if a linux iso will provide the "try X
without installing" option? From https://ubuntu.com/download/desktop
for example or https://lubuntu.net/downloads/ it is not clear which
will give that option. (My expectation was that all could "try
without installing" but recently I tried some which excluded that
option from the boot menu)
I don't think there is any general way to tell if a linux iso will provide the "try X without installing" option.
But I know that all Ubuntu Desktop and Ubuntu community flavours release iso files that provide the "try X without installing" option.
mini.iso and the Ubuntu Server iso files are exceptions. You can consider those iso files to be 'only installers'. The Lubuntu Alternate iso files (most of them have passed end of life now) are also 'only installers'. They use the same text based Debian installer as the Ubuntu
Some linux distros provide both iso files for live USB drives and for plain installers (for example Debian and OpenSUSE).
Please notice that lubuntu.me is the official web site. The Lubuntu web site that you refer to is not up to date.
Any bootable USB drive
Some people could say that any bootable USB drive is a live USB. But I think most people mean that a live USB drive can do more that only start an installer.
A USB system that is cloned from an Ubuntu
mini.iso file is only an installer. See also this link and scroll down to 'How to make an Ubuntu Minimal USB using dd'.
Live USB systems
Most live systems run the operating system so that things are stored (temporarily) in RAM.
A USB system that is cloned from an Ubuntu Desktop iso file is a typical live USB system. You can use it to try Ubuntu and install Ubuntu.
Persistent live USB systems
Persistent live systems use an overlay method to store those things in a file or partition (Ubuntu uses the file name or partition label
Methods and tools are described in this link.
Installed system in a USB drive
You can also create a fully installed system in a USB drive. Like a cloned live system it is also portable between computers. Some people may say that such a USB drive is also live, but I would say it is 'installed'.
A method is described in this link.