It is worth a try, but it might just end with a big frustration.
I don't think that Plex Server has a compatible hardware profile for Panasonic devices. So playback might not be working at all.
Install Plex Server on your dad's PC. Sign in his server into his own plex account. (If he doesn't have one, yet, he must create one). You share your server with his plex account.
After you have verified that your dad can access your Plex Server using the web app on his PC (i.e. the 'normal way'), you activate DLNA on his Plex Server.
IF everything is working, he should see a DLNA server (when browsing with his Panasonic device) with 3 folders: Video, Music, Photos
then 'Shared Video'
He needs to have his PC on all the time.
Given the many IFs and WHENs, it might be easier to just give him a Raspberry Pi3 with 'PMP embedded' on it. Or maybe a Firestick or a Chromecast.