Shotcrete is a placement method for concrete. Lightweight concrete usually ranges from 90 to 115 lb/ft3 (1400 to 1800 kg/m3). In wet-mix shotcreting, lightweight concrete should use presoaked aggregate to make the mixture pumpable. When it’s pumpable, as with conventional concrete mixtures, it is then accelerated to a high velocity by air at the nozzle and projected onto the surface. Lightweight aggregates can also be used directly in dry-mix, and there you don’t need to worry about pumpability because the dry materials are conveyed through the delivery hose. Water is added at the nozzle.
Here’s the specific reference on lightweight from ACI 506R-16, “Guide to Shotcrete”:
18.104.22.168 Lightweight aggregates—Lightweight aggregates should conform to ASTM C330/C330M if used in shotcrete. The aggregate should meet one of the gradations shown in Table 1.1.1. Wet-mix shotcrete with lightweight aggregate is seldom used and is difficult to pump because the aggregate absorbs water, which reduces the consistency of the mixture. Presaturating the lightweight aggregate before batching improves pumpability. Lightweight aggregate mixtures have been shot for wall and floor construction. Shotcrete is frequently employed for fireproofing structural steel members using lightweight aggregates in the mixture.
We suspect that cellular concrete cannot be shot because it uses injection of a pre-formed foam into a cement slurry and is highly fluid. That would preclude any stacking of material to make a vertical surface, and would instead just be pumped in place like a high slump concrete.