Connecting the lithium bank straight to the existing alternator.
Always through a current-limiting DC-DC charger, sized as above.
Charging
Put a DC-DC charger between the alternator and the bank, sized to the smaller of a quarter of the bank's capacity and half the alternator's rating. Connecting a lithium bank straight to an alternator is what destroys alternators.
An empty LiFePO4 bank behaves electrically like a very hungry load. It accepts everything the alternator can produce and keeps asking until nearly full. A lead-acid bank's internal resistance rose as it charged, and that rising resistance is what protected alternators for decades.
Take the smaller of a quarter of the bank's capacity and half the alternator's rating, then round down to a size you can buy. A 300 Ah bank behind a 90 A alternator gives min(75, 45) = 45, so a 40 A charger.
Badge ratings are usually cold, high-rpm bench figures. An old, small-case or poorly ventilated alternator sustains less, and the charger should be sized against what it can actually hold all day.
So it charges only with the engine running and cannot drain the cranking battery into the house bank at anchor.
Run the engine with the bank well down and check how hot the alternator gets under sustained charge. This is the test that tells you whether your sizing was right on your boat rather than on paper.
Above about 120 A of alternator output, DC-DC chargers become expensive and need paralleling. An externally regulated, temperature-sensed alternator specified for lithium is the better answer at that scale.
Connecting the lithium bank straight to the existing alternator.
Always through a current-limiting DC-DC charger, sized as above.
More on charging
Take the load estimate, charging sources and cable runs to a qualified marine electrician. Our installation guide helps you ask about isolation, over-current protection, ventilation and compliance before work begins.