Very nice image!
My guess is you're trying to pull too much tonal variation out of too little variation in the data.
Assuming I'm right, here's the (cocktail napkin version of the) problem: Originally, the tones were very close together, so their digital numeric representations were quite close in value. When you then try to stretch them out, the tonal values are scaled (the computer doesn't "know" this is supposed to be a smooth gradient, so it doesn't interpolate). This scales their difference, producing a noticeable gap in the two tonal values. Since in a smooth gradient this change occurs along a line (an "isoquant", if you will), the boundary is obvious to our visual system as an abrupt step.
I often use two solutions to this: one is to introduce "grain". This randomizes the transition point and destroys the organization of the isoquant or "line" where the transition occurs, hiding the problem. The success of this approach depends on the size of the step and the amount of grain you will tolerate. I don't use LR (I'm a PS type). In PS, go to Filters->Camera Raw Filter...->Effects and dial up Grain, Size and Roughness until you don't see it anymore. I'll let you research the effects of the three inputs...mostly cuz I don't know off the top of my head.
My other solution is to borrow from the architectural photographer's toolbox and composite in a sky. As long as you get a reasonable match in the lighting direction, this works quite well.
Whether this helps or not, I hope that you find a solution.