There is a reason why so many manufacturers have moved to DIT engines and CVT trannies. And low-speed pre-ignition has been a problem with these powertrain combos. RPMs are kept as low as possible for fuel efficiency and emissions reasons. You have the ability to keep things in higher rpms if you like, just adjust your driving style.
I would always tell my son that if he wants to accelerate quickly hit the downshift paddle (to raise rpms) then push moderately on the throttle. If you just mash the throttle from a low rpm cruise you will create the conditions for low speed pre-ignition to flourish. Get the rpms up, and then load up the engine, not the other way around.
Don't be afraid of redline or high rpms, these motors have such a low rpm limit given their small size, they could easily rev to 7k+ if the manufacturer allowed for it, but there wouldn't be much benefit in terms of power levels, though it would be perfectly safe.
TLDR, you will never get peak power from the LX sedan without entering Sport mode and pinning the throttle to redline. Whether or not you care about doing so, is up to you. (It's probably worth it to trigger it at least a few times just to make sure you know HOW to do it if you feel like it, but that's just me.)
The boldfaced comments are why I sought out the six-speed manual for this car, LOL. Well, for the Sport Touring HB - there is no manual option for the Civic sedan without going to the Si.
That said, with the 1.5T there is no benefit to running my ST to redline - short shifting at 6000 RPM is about right (peak HP).
With the 2.0 NA engine in the LX, I believe what power there is, is delivered linearly to redline, as peak horsepower is at 6500 RPM.
If fuel efficiency is your primary concern, of course, you can just stay under 4000 (or 3000) RPM to get max MPG out of the car, you'll just never really accelerate very quickly (whether from a full stop or to pass at speed).
The CVT will optimize for the latter, which is why you would not see the RPMs in the LX go very high even in "Normal" mode (though what you described in the OP sounded a lot more like "Econ" mode).