The next step was to correct the perspective. Lightroom (and Camera RAW) have a new and very useful feature called Upright, that helps to level images and correct perspective. In order to use it you must first enable Lens Profiling. Then you can choose from Automatic, Level, Vertical or Full. I first went through all these presets, but none of them did what I wanted. Either the result was too cropped, or too weird. However, all was not lost, because I also had the option to go fully manual in my correction efforts.
>> I should state that I have used this feature quite often with just the presets, and have been VERY pleased with the result. In this particular case, I think the Samyang lens, height of the tower and low camera viewpoint all conspired to make Lightroom a tad confused. <<