Upgrading between 2 LTS releases will be available on .1 point release of the later release. In this case, you'll have to wait until 16.04.1 is released, which, according to release schedule, will come out on July 21st.
But upgrading using live ISO is not possible. Upgrading system will need individual packages to be installed. You'll have to download another type of ISO called alternate ISO which installs packages from CD. In the past, Ubuntu used to provide alternate ISO for desktop flavors, but it's not available anymore. For server flavor, alternate ISO has been the only available ISO for downloading. In your case, I think you should upgrade over the internet as ISO you downloaded is useless anyway.
I personally never upgrade between 2 LTS releases but have upgraded between 2 consecutive releases from 13.04 all the way up to 16.04 today. Of course, some problems do pop up, but with the power of Google, I can fix those problems. If you're upgrading a desktop, don't hesitate to try. If anything goes wrong, you can always reinstall. But if you're upgrading server, you may want to set up test server before proceeding to upgrade.
If there is grub, it will detect any previous version of ubuntu so an upgrade should be a straight forward affair.
– Jenson Pais Apr 29 '16 at 05:03