Comment from someone who doesn’t know anything about this plugin.
The output from datetime depends on the corresponding translations in WordPress core. I don’t think you want to mess that deeply (and change ALL occurrences of abbreviated months to lowercase).
A nice solution would be to use CSS to force lowercase just for this date. For that to happen nicely, it would be great if the developer of this plugin could add a SPAN element with a specific CSS class for the date. (Perhaps it is already possible to assign a class in the plugin settings, I really didn’t check).
You would then use something like the following under Appearance → Customize → Extra CSS
span.last-modified-datetime {
text-transform: lowercase;
}
(But for this to work, the HTML would first need to have the corresponding markup, obviously).