The only tool in iPhones built in camera roll editing software in my opinion is the brilliance slider. This is a very helpful tool, and when used with caution, can yield great results. I wonder if Adobe has ever considered adding their own version of a brilliance slider?
Brilliance:Adjusts a photo to make it look richer and more vibrant, brightening dark areas, pulling in highlights, and adding contrast to reveal hidden detail. The adjustment is color neutral (no saturation is applied), but there may be a perceived change in color because brighter images with more contrast appear more vibrant.
Sounds like the equivalent of bumping up 'Shadows' and 'Contrast' while reducing 'Highlights'. LrC gives a much finer level control over these settings and you could make a presets that would match the amount of 'Brilliance' you want to add.
I can certainly understand why you would think that lightroom, with its finer controls, would actually deliver a superior image. However, I can assure you, that is absolutely not always the case. I have been using lightroom for over 10 years and am fairly well versed in the editing tools. I tried to emulate the results I got with apples brilliance slider on a sample image, and I was not able to, and gave up after 5 or 10 minutes. If you'd like, I'd be happy to upload an untouched iphone DNG image, a JPG of the brilliance slider effect, and you can have a go at it yourself. If you are able to get the same or better results, than I will certainly have something to learn from you.