According to the links in the previous issue we touched upon this subject, implementation could be as simple as adding a hook if a base url is configured:

app->hook( before_dispatch => sub {
        my $c = shift;
        unless ($c->req->url->path->to_route =~ m#/baseurl#) {
            $c->req->url->path( "/baseurl" . $c->req->url->path->to_string);
        }
    } );

(https://stackoverflow.com/questions/25170147/base-url-in-mojolicious-template-rendering)

The bigger question is where to put the base url config?
I honestly don't think this is a setting that would be used much, and it can't be set from the web interface since you likely won't have access to it, so it'd probably be fine in lrr.conf. Might also want to add an environment variable override for Docker users?

You already have a hook into before dispatch, and that module has access to the LANraragi settings module. I was testing it out but couldn't understand mojolicious' url object. Had some wierd behaviour with url->base that would make it use the wrong address, and also the web app pages didn't seem to exist at the rewritten locations.I couldn't figure it out after a few hours.

Oh yeah, the SIGTERM catcher does hook in before_dispatch.
You can add code in there no problem normally, I still think it'd be better/easier to put the base url setting in lrr.conf, you could then access it with something as dumb as $config->{base_url}.

If you can't get stuff working in a hook, I think Routing.pm would also be an acceptable place to try? You could store the base url setting in a string (defaulting to empty of course) and prepend that to each routed URL path.