I took a different tack by lightening the background because the crane is already getting lost in the dark colours. The first two were exported as TIFF files to Viveza (a Nik plug-in) without any extra processing in Lightroom. Viveza has control points which basically create feathered masks based on similar colours within a set distance from the control point. The trick was to set control points that didn't include the crane's neck, I used 5 and 6 control points, but I could have set a couple dozen control points with small ranges and changed settings for each control point instead of a group like I did, to get better control over the final result.
The first copy below has brightness increased for control points in the background trees and the horizontal brown line just in front of the trees. The second copy has just the background trees as control points, but along with increasing brightness, I decreased contrast and warmth (I think warmth is a combination of colour temperature and hue, but I'm not sure). The third copy is only processed in Lightroom, with only clarity adjusted. Once I finished editing in Viveza, I then set clarity in Lightroom to +30 for all three copies and I increased sharpness in Lightroom on the first copy from the standard setting of 25 to 54.
The main problem that I see is that the crane's neck is very close in colour to a lot of things in the background. I tried changing red, green and blue levels, saturation and white balance, but I didn't get anything that looked natural or was an improvement. It is possible to get better masking with photo editing software like Photoshop or Gimp, but that requires a much bigger investment of time. Next time tell the crane to come back when the sun is out and get him (her?) to stand in front of a big patch of dark green bush that is in shadow.