Sounds like you're all set, LOL. Cool. Actually, your use of lanolin-based treatment works well for leather. I'd be very hesitant of a hand cleaner, though, as the detergents and de-greasers don't help the leather fibers and will weaken the fibers.
But, any high-percentage lanolin lotion/oil/wax is good. Leather treats lanolin as a natural oil, although it doesn't absorb as quickly as a neatsfoot.
You want the treatment to get into the leather, not just moisten the surface. The surface is finished, as a result, the treatment needs absorption time to get through the finished surface to the underlying fibers where most of the stiffness is occuring. This takes time and several applications, especially since you can only treat one surface, where I usually treat both sides of my leatherwork to speed things up.
Even though you have a black interior [which makes things much easier, LOL], you want to control the absorption process. Otherwise, some darker areas may occur. [Not too critical for black, but thought I'd mention this]. And, since you have nice weather, absorption should be quick.
I control absorption by applying the treatment, let sit for around 3-5 minutes, and wipe off excess with a soft towel. Leather has it's natural absorption rates, which differ across the leather hide. Your conditions seem to indicate 2-3 minutes.
Then, re-apply, and repeat for a few times. Let it dry [absorb] overnight, and check how it looks the next day. Repeat process until desired softness and colorization are to your liking. Getting the leather soft will most likely darken the color noticeably.
Products like armor-all, maguire's, saddle soap are primarily good for surface after-care, but ineffective in penetrating to the fibers, where you need to get to.
Most horse-tack cordwainers use neatsfoot or some lanolin-based paste/oil to soften their tacks. Oil for the primary softening, and the paste for after-oiling through the leather's usage. They also try to keep the leather warm, around 70-75 degrees ambient, to maximize the treatment. Too low, lower absorption, too high results in spotting.
Sorry if this is a bit long, but I've had great success in leather conditioning with the above. And, as you posted, I'm taking your query from reconditioning a very dried-out leather cover, not a general shine-up.