Description
The "Getting Mosh" section on https://mosh.org/#getting says the Homebrew version can be installed on OS X 10.5 or later. Unfortunately, my old Mac running OS X 10.7.5 can no longer run Homebrew at all (it used to be able to, but Homebrew stopped being able to update itself and now the old client can't talk to their servers) so I don't think it's fair to say it's still possible to install on 10.5 via Homebrew. Homebrew's own site now says 10.13 is required.
I can however confirm that MacPorts is still able to install Mosh on 10.7.5 in August 2020, so I have no reason to think the requirements have changed there. So perhaps MacPorts is now a better option than Homebrew if you need to put Mosh (or other tools) on an older Mac.
(The Chrome version of Mosh also fails to install on Chromium 49, which is the last version of Chromium that will run on OS X 10.7.5. But I could install Mosh on a Debian 8 image that the old Mac has installed in Vagrant/VirtualBox, and use it by doing for example vagrant ssh -c 'mosh srcf' so that might be one alternative to MacPorts if necessary.)
It's a pity that Macs are premium pieces of hardware that can last 10 years but tend to get software support for only half that time.