If you can run all you need with 200Ah than you would need 200Ah of lithium minimum, you would get a longer life if you only use 80% of the batteries capacity but they will still give 1,000 cycles if used down to 0%SOC. The capacity would become an issue if you have an inverter that draws a very high current, a 2500w inverter at full load would demand 230 amps, well within the lithium’s ability to supply but if the current draw was for an extended period the battery life would be shortened, 0.5C is the discharge rate Winston use for their life cycle testing so a discharge rate higher than that is unknown territory.What I am saying is say I have 400 AH (AGM) battery bank at present, that is at least 200 AH usable. Of that I run all I need to, but if they were Lithium I would only need half that (100 AH) to run the same equipment. And that is what I meant with the "Or do I have this wrong?".
The charger depends on what charger you have now, if it was compatible with US Gel batteries it will be fine, you would need a battery monitor that could count Ah in and out, not one that makes an estimate based on voltage, the inverter depends on what appliances you want to run but it would exactly the same inverter for any type of battery chemistry that is nom. 12v. The only additional monitoring is a cell logger to display individual cell voltages and sound an alarm if a cell goes outside the boundaries, about $50 including the plug and cables.
The system is as much a fit and forget as the one you have now, you can't just forget about how much you discharge the batteries or their minimum voltage but an alarm would sound if you went too low so possibly less attention required than the ones you use now. The other end of the scale, they never really need to be recharged to 100%, it's more for resetting the battery monitor so you know where 20% SOC and 0% SOC is, the cells will discharge below 100% capacity but you are headed into rapid cell voltage drop past this point, but again, an alarm would sound, an alarm would also sound if you over charged the cells for some reason like using a charger that isn't set to suit the batteries, if you were there to turn the charger off when the alarm sounded you could charge the lithium batteries with any charger. we have developed an automated system that turns the charge off if an over voltage alarm sounds so correctly wired up you could potentually use and charger, I wouldn't do it though. In my books the cell logger and alarm is a safety back up system, not a primary control system, belt and braces stuff I guess.
T1 Terry