If possible try not to use Apples Recovery Servers, in October 2019 the certificates for
several OS's expired and Apple have not updated these on the Recovery Servers.
I take it you want High Sierra to run on one partition and Lion to run on another.
First thing to do would be to create a new partition.
Boot to the Recovery HD and open Disk Utility.
As you are running High Sierra it may be formatted as APFS, if so click on
View in the menubar and select Show All Devices.
Now select the Disk in the left panel (called Apple HD..... or something similar.
Click on Partition, use the toggle on the circumference and drag to the size of
partition you want. On the right give it a name and make sure the format is set
to Mac OS Extended (Journaled), click Apply.
Once that is done boot back to your mac normally, click on this link,
https://support.apple.com/kb/DL2077?viewlocale=en_US&locale=en_US
This will download InstallMacOSX.dmg to your Downloads folder.
When downloaded open to InstallMacOSX.pkg, double-click on
that and an installation window will open, this does not install Lion
but converts the InstallMacOSX.pkg to the Install OS X Lion.app which
you will find in your Applications folder, it should be 4.76GBs in size.
(You may get a warning about invalid certificate {Apple are useless} just
continue and the conversion should happen.)
Apple only released this version of the Lion install .dmg in June 2021.
Prior to this you would need to buy it for $20 from Apples Online Retail Store.
Once the download has completed you now need to create a bootable USB installer,
Apple does not have an official way of doing this for Lion but there is a free app you
can try here, http://diskmakerx.com/whats-this/
Click on the Downloads section and scroll right to the bottom of the page you should see
Download DiskMaker 2.0.2 (Zip File about 3MBs)
Click on the text and it will download the zip file to your Downloads folder.
It may open automatically if not double-click on it to open it.
Open the app and follow the on screen prompts, use a USB flash drive (8GBs or over in size).
When the USB installer has been created Restart your mac while pressing and holding down the
option/ alt key. In a minute or two you will see the Boot Manager, select the Bootable USB
and press Return. When you mac boots to the USB you can then start to install Mac OS X Lion
follow the instructions carefully and remember to select your new partition as the destination for the
install.
