How much space is needed to install Mac OS X 10.7 on to an external drive?

I would leave space for some apps besides just the operating system, but each could use 10GB as a bare minimum, so 12 GB volume would be required, so leaving a bit of space for a utility or two, I would go with 16GB each partitions.

This external drive would have to have a GUID partition table, so an old drive from a PowerPC based Mac using Apple Partition Table or anything Windows related won't do, as the drive would have to be bootable. Of course these two volumes must be Mac OS Extended (Journaled).

That's easy with either CarbonCopyCloner or SuperDuper (SD is free if you only use the mode to create a full backup, i.e. can't update the last one). Just oot get an external, format it with Disk Utility as Mac OS Extended (Journaled) and GUID partition scheme, install one of the two, launch it and follow directions. When finished, test the bootup capability by choosing it as a startup disk in System Preferences. If it boots (will be a bit slower than the internal), try a couple of apps, and then boot back into the internal. Done.

Another option that does not require a reboot onto another partition is running Parallels Desktop and installing Mac OS X 10.7.x Lion onto a new virtual machine and installing the app there. Then if you need to run the app, just launch Parallels Desktop to resume Lion and the app and go, no interruption.

So, that's great - if you install a bootable 10.7 and whatever other software, make sure that your Mac can actually boot from 10.7 - Macs cannot boot with any OS version older than what they came with (and it doesn't matter if that is on an external or internal disk).

That is true but the installer won’t let you proceed with an installation that won’t boot your Mac. On the other hand, a program like DiskMaker X will allow you to create a otherwise bootable volume for an installer needed by a supported model Mac. I have a series of USB flash drives than can install High Sierra and lower operating systems on those needing this function to format perhaps a new drive and put in an operating system.

installing Mac OS X 10.7.x Lion onto a new virtual machine and installing the app there

This would be in violation of the SLA as it specifies that you can only run a copy of your currently installed OS as a VM - not a different version - see page 2 of the SLA (Section 2 B, iii):

https://www.apple.com/legal/sla/docs/macosx107.pdf

That is true but the installer won’t let you proceed with an installation that won’t boot your Mac.

I was not referring to an installer - I was referring to a bootable clone. I much prefer a fully and independent bootable clone which can be used to boot into and then format a disk and clone back the OS (which can have all the apps you installed, etc). I have a plethora of bootable clones going all the way back to Snow Leopard and all created from out-of-the-box fresh installs (some with/without added applications); but, they all need a machine that will support booting with them.

Well, it really doesn’t matter if you agree or not. That is what it says and you agree to it when you download the OS and use it.

And, I do not need to nor could I explain why third party software developers allow you to do something - you might want to ask them. They may not know that you are about to violate the licensing agreement. After all, that is a matter between you and Apple.

It isn't really so much about which one you originally bought - they now have a background process which checks not only any software you have installed, but also matches the computer to the Apple ID and OS versions you've had - it checks the serial number as well as the firmware.

Recovery is great and I'm glad to hear you got it all done. FWIW, neither Lion nor any later OS versions came with disks - that is when they changed to the download only model. Snow Leopard was the last OS to come on a disk.

Without its' own partition, you cannot install two different OS versions on the same drive and expect to boot from either one (at least that is what you were wanting to do in your first post).

Read 2-B-iii and I don’t agree. Also please explain why Parallels and VMware allow you to do so.

Edit:

You may want to create a backup - either with Time Machine or a bootable clone on an external drive as that will make it much easier to recover from a disaster.