That outlet is a mess.
It has a big four conductor wire running into the box and only the black and white are used. No ground wire at all.
I'm guessing my father did this back in the 80's.
Before modifying it in any way at all, I would trace that cable to where it comes from. My guess is that the other end also has only the black and white connected. To add a ground, you'll have to connect the ground at both ends. That's not too hard, assuming everything else is grounded. But if the box where that cable comes from is also not grounded, you'll have to connect ground there as well, and so on back to the main panel.
From your description, it appears to me as if the outlet was added by someone else after most of the wiring was already done. It may have been your father, as you said. But whoever added it thought the ground was not important. Possibly they thought that outlet would only be used for a lamp, which doesn't even use the equipment ground. Or, possibly they thought grounded outlets were a new-fangled thing and not worth the effort to run a third conductor, since for so many years nothing had that extra ground wire. I've seen whole houses wired that way, with every ground wire cut off in every box. In fact, I've rewired a whole house that was wired that way, re-using each wire in a place where a slightly shorter wire was required, so that it would be long enough to connect the grounds which were originally cut too short to connect.
If the red wire is not being used for anything, you could cap it off at each end, or you could replace the whole cable with one with only two insulated conductors, and re-use the 3 conductor one someplace else where you need the extra conductor. That looks like 14-gauge wire to me, so it should be relatively cheap and easy to work with, but if the circuit is 20 amps, it should be 12-gauge instead of 14. Truthfully, you'll probably be OK leaving it at 14-gauge even if it is a 20 amp circuit. I've seen whole houses wired with 14 AWG, where the original 10 or 15 amp fuses had all been replaced with 30-amp fuses, and the wiring operated for years like that without causing a fire. But you have to be aware that the probability for a fire is higher than if you used the correct size wire, and also that after such a fire, your insurance company may not cover the loss if they are aware that you were aware the wire size was too small.
20-Amp circuits with 12 AWG wire are the norm around here (Oklahoma), but I'm well aware that in a lot of other areas, 15-Amp are more common because of the thinner and cheaper wire required.