You have curves in LR which is are precise to use. I use the shadow slider with the black clipping indicator on and then I readjust the shadow level with the small slider on the curve itself. What can be an issue is that the default level of 5 of BLACKS in the BASIC panel is too high. Simply bring it to 0 or 1 and then readjust your black point as indicated above. It works for me. The only tricky part for me was that the densitometer readout values in LR are presented in % and after years of using level values in PS (0-255) it can take some time to adjust.
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No, this is not the same thing. When adjusting those sliders you are not altering the relationship between RGB channels at the left end of the histogram and balancing them to black, you are merely clipping the channels in their current relationship to each other.
I'm speaking of something similar to the WB dropper which takes your click point and adjusts the RGB channels so they meet at that point (all three values equal). This doesn't neutralize the RGB relationship at the left and right ends of the histogram, just at the tonal point you chose.
What I'm doing is making an image look as best as I can in LR using calibration settings and tonal adjustments. It looks good but there's still a slight cast in the shadows (usually red). If I want to perfect the image, I have to take it into PS, open levels, find where the shadows start to clip and then move the RGB channel sliders separately to get the clipped area to be true black (or closer depending on the image). This gives the image the final POP that it needs.