Fate/Zero(25 episodes)—Being that your dad likes LotR and Star Wars, I'd recommend this the most. I wouldn't say it’s necessarily action-packed, but when there is action (fight scenes and what not) its of very high quality.
I've seen episodes 1-12 so far, and believe me when I say, when you watch this, you don't feel like you're watching a typical anime. The only thing is, the first episode is about 50 minutes long and is basically just setting the stage for the rest of the show. He might get a little bored out of that, but if he likes LotR, I don't really see what the problem would be there.
Psycho-Pass(22 episodes, with a second season on the way)—If you were to combine Criminal Minds and 24 and set it in the future, you'd get Psycho-Pass. It doesn’t really match up with the other stuff your dad likes, but I think it’s worth giving a shot. It's and incredibly good and intense show that presents allot of interesting questions about morality, law, government, etc. It starts out a little episodic, but eventually becomes very serialized. The whole presentation of this show is pretty different from other anime.
Cowboy Bebop(26 episodes)—I don’t think I need to explain this one.
Btooom!(12 episodes)—People fighting against each other to survive on an island, while the people who put them there watch for their own entertainment—that’s basically what the show is about. It’s not an incredible show, but it’s not bad either. The major problem I have with this one is that it doesn’t have a very conclusive ending.
Darker Than Black(around 40 episodes if you include both seasons and a four episode OVA—which is definitely worth watching)—Darker Than Black is kinda hard to explain so I’ll leave it to you to look up on it.
Gungrave(26 episodes)—Think of Cowboy Bebop mixed with Breaking Bad, plus add mutant monsters. Aside from being very serious, with little to no comic relief, it’s a pretty good show, though personally I think Cowboy Bebop is much better (and it doesn’t hold a candle to awesomeness of Breaking Bad, but we’re talking about anime so….
but if you haven’t seen Breaking Bad you NEED to watch it, so does everyone else on this planet!)
All of these shows fit your parameters the best, I’m gonna briefly list a few more that you might be able to show him, but don’t necessarily fit what you’re looking for exactly.
Steins;Gate (24 episodes + and OVA and a movie)
Death Note (37 episodes)
Eureka Seven (50 episodes)
Guilty Crown (22 episodes)
Code Geass (50 episodes)
Attack on Titan (25 episodes)
Gundam 00 (50 episodes)
Black Lagoon (24 episodes)
Baccano! (16 episodes)—Can’t say I’d recommend it, but…
Every anime I've mentioned is English dubbed.
Is there anything content-wise that your dad would really object to, because a few of these shows might be a little iffy depending on what he is willing to tolerate?