They have color correction sliders for yellow-blue and green-magenta but not for red-cyan, unlike in Photoshop. It is really annoying to go into Photoshop when I need to make those simple adjustments -- does anyone know a reason this isn't included in Lightroom?
If you look at any color wheel, you have two axes on the wheel:
To correct any color cast, this is usually enough. You can correct the main source of color shift in natural light on the temp axis (blue/yellow), and then do the fine tuning on the tint axis (magenta/green). Tint most often occurs through artificial light.
magenta red | x--| | | yellow ----+---- blue | | | cyan green
The axis you propose is actually 45° off these axes, you could also correct any cast in this direction by using the other 2. However, this also explains why there is no 3rd slider: using it would always affect the temp & tint as well, although it would be easier with it to correct such a color cast.