I’d imagine:
Alternator to starter.
DC Cable from starter goes to Automatic Charge Relay (ACR). This only allows
current to pass if either side is over say 13.2V for x minutes. An ACR would, if house banks are in great shape also charge your starter.
The ACR cable goes to a common DC bus.
Yacht 12V loads run off DC bus via your DC elec distribution board.
If your
lifepo4 have own BMS then it also simply connects off the DC Bus.
You seem to have another lead acid bank, probably it sits with a DCDC controller also onto that DC Bus.
The battery inverter likely can:
1. Take shore AC
power.
2. Take
generator AC
power (unless you have a rectifier in which case the gennie supplies DC to that DC bus).
(note that 1 and 2 would be an either or via a switch on AC panel so as cannot run gennie and
shore power concurrently)
3. Take DC from that DC bus to supply your AC
electrical distribution board.
4. Take DC input from solar for mix of live use as AC and charge input to the DC bus.
If your
lifepo4 battery is 52V then need a 52:12 DCDC controller between it and the DC Bus so that can keep your 12V loads on the old DC bus and then the battery inverter is likely also 52V and it would be directly connected to the 52V lifepo4.
Obv fuse protected everywhere, and I would have Ah meters via shunts at the Neg pole of the lifepo4 and acid house bank.