Yes you can use 3s li-ion to augment your trojan batteries. I have a 312ah li-ion batterybank (3s) that augments my 220ah 4s lifepo4. And previously I used a 94ah 3s li-ion pack(handbuilt with 18650) that augmented my 102ah agm battery.
As long as the lead acid is charging from the solar panel you can connect your 3s(as long as its not empty) into it, and it will charge that way or you can use a boost/buck converter to charge the 3s which is a safer way to do it since the boost/buck can be set to 12.6 volts and limit the amps. Just don't charge while the solar is not producing power because the li-ion will drain the lead acid until they equalize.
Li-ion is the 18650 cylinder cells, lipo is the more dangerous pouch packs. 18650 is just as safe as lifepo4 as long as you don't overcharge or puncture them. Make sure you have a good hi quality bms, that you tested to work on you li-ion pack.
When the solar panel is producing power and your batteries are about the same voltage (example 12v agm, 3s li-ion or 4s lifpo4) you can connect together, whichever battery is the weakest will receive the most amps from the solar system. I connected agm, and li-ion to my lifepo4 to topped them off, with no sparks or other type of problems. Just try not to connect a completely depleted battery to the system because the depleted battery will also start draining the full batteries. It's why I use a boost/buck converter that can limit amps output.
Picture of my first 3s 94ah li-ion pack (168 cells), this was a solid performer, I retired it when I moved to lifepo4.
View attachment 28109
This is a picture of my 312ah li-ion batterybank. I use the mobius 26ah battery pack and connected 12 of them in parallel. I spent about 450 dollars to buy all 12 of them. I charge this from my lifepo4 battery with a boost/buck converter. The only weakness of this pack, is you need to have a good charging system to charge something this massive. With limited sunlight this pack has been at 10 percent (about 10 volts) for the past 2 weeks. But even at 10 percent it still runs my 200 watt inverter and my 12 volt fridge. Everyday I charge just enough to get me through another day, my lifepo4 is not much better at 20 percent, my 240 watt panel/20a mppt is barely charging over 500ah of lithium.
View attachment 28110thanks for the info. One thing I forget to mention is that my rv does not have an inverter as it requires shore power for the ac to work. So I'm all 12v for any boondocking unless I run a generator.