Can I install a version of photoshop and lightroom CC that will work on High Sierra?

this has somewhat confusing replies, but to summarize the correct responses, you can install and, with a current subscription, use older compatible (with your 64 bit os) cc apps. almost all cc 2019 (and older) app installers can be downloaded from prodesigntools.  you can browse the available apps and versions without any subscription.  it is not necessary to install the cc desktop app to use these versions.

but for cc services, you will need the adobe cc desktop app. the cc desktop app will install on os'es as old as win 7 and mac 10.11 (and earlier, but i don't know how much earlier) usually automatically by going here,  https://creativecloud.adobe.com/apps/all/desktop?action=install&source=apps&productId=creative-cloud 

but if you have trouble downloading the cc desktop app or you see an error message when trying to install, and use the alternative download links at page bottom here, https://helpx.adobe.com/in/download-install/kb/creative-cloud-desktop-app-download.html

NOTE: you must have a 64 bit os to use most of the adobe apps.

CC2018, 2019, and 2020 will run on High Sierra.

1. you can install the latest and 1 version prior versions using the cc desktop app. you must have a subscription because previous versions are not available with trials. other versions are revealed after clicking file preferences>apps>tick show older apps (at panel bottom).

2. for versions cc 2019 and older, use prodesign tools.com*.

3. for versions newer than cc 2019 but older than one previous version, contact adobe support for links.**

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* most (but not all) adobe download links are available from prodesigntools.com. https://prodesigntools.com/adobe-direct-download-links.html

follow the directions (esp, step 1)

save the install file. it may not remain online.

thank jim @ prodesigntools.com
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** there are 3 ways to contact adobe; chat, phone and twitter:

chat:
use a browser that allows popups and cookies, and click here, https://helpx.adobe.com/contact.html?rghtup=autoOpen
in the chat field (lower right), type AGENT
be patient, it can take quite a while to reach a human.

phone:
https://helpx.adobe.com/contact/phone.html

twitter:
tweet @AdobeCare

p.s. if you're contacted by anyone (via email or private message), it's much more likely to be a scammer than an adobe representative. ie, double check for an employee badge if contacted in the forums and look for an adobe.com domain in the email address if you click reply to an email. then check again and be very suspicious. any other method of contacting (or offering to contact you) is almost certainly a scam,

https://community.adobe.com/t5/using-the-community-discussions/adobe-support-community-guidelines/td-p/4788157#:~:text=constructive%2C%20and%20encouraging.-,3.%C2%A0Be%20Safe%C2%A0,-Do%20not%20share

I don't know if the Cloud Manager will install, but the only way to get a version that old is not direct from Adobe

Adobe now offers the current and ONE older version via the online program manager

Go here for all older links https://prodesigntools.com/adobe-direct-download-links.html
Prodesigntools is an official Adobe partner, and the links go to Adobe, not a 3rd party site

i disagree with the previous response. while you cannot install the latest versions, you can install previous versions.

As far as I know... No

See https://helpx.adobe.com/creative-cloud/system-requirements.html