Yes and no.
LPL is primarily a pre-wax cleanser - it's actually the better cleanser of the two, but also leaves oils behind for the wax to bond to along with some fillers (like a glaze).
BH is primarily a glaze - it contains more fillers than LPL (so will mask more swirls than LPL), it won't cleanse as well as LPL but does contain mild cleansers too and leaves the same oils for wax bonding.
I didn't say the do the same, but actually... they really do, as it happens (see above). They just do each thing to different degrees and will achieve difference results with each hence my opinion would be that both is unnecessary and a preference for a proper (perhaps corrective) polish instead (although maybe I didn't make that bit clear). Now if you'd suggested using Lime Prime (rather than Lite), I might see the point of using both due to the abrasives in LP. However, this is just my opinion.
Just speaking from personal experience as I will only recommend what I've used and not what I have read about, Lpl can be just waxed over but I find it too oily , it is however a good way to cleanse and bring life back to the paint. I would not advise using Lp on a Nissan or without seeing the paint or what someone uses to polish with including their method, I couldn't recommend anything abrasive incase of damage
It was overkill and I'm sure as the op has opted for - clay, black hole, supernatural. They will give impressive results
Ps. I have tried nattys but I just can't get the reflections I get with supernatural
Other favs inc blacklight and hybrid v7