> What is the benefit of adding lead if you don't fully discharge the lead? Or do you?
You do - but not always. If you only discharge the lead 1/10th of the time, your lead batteries will last incredibly long (if otherwise properly maintained).
Additionally, lead doesn't take up charge quickly. Putting in Lithium allows you to take full advantage of your solar. This can be mitigated in other ways, but this makes it "easy" and a not complex system with many charge controllers, many batteries, etc...
Additionally, it allows your input voltage to be much higher (from the solar) meaning you can have smaller wires (but amps are amps!).
> If you are only using the lead until the LiFePO4 are dead then what is the benefit? Or do you have something to disconnect the batteries with they are at 50% (or what 55% to be safe) charge?
I'm not sure what the question is, sorry. Yes you have equipment to make sure you are safely drawing from the lithium and safely charging the lead.
> So you can increase the battery capacity by 50% of the lead you buy instead of 100% LiFePO4. Which means the lead needs to be half the price or less (excluding the cost of the DC-DC charger) for it to make sense.
Well, if cost is not a problem, it would be better and a more simple system if you bought 100% LiFePO4. But that is really expensive.