DC to DC charger question

I have a slightly unusual marine system. The primary system is quite standard with a starter battery for the pair of engines and two house batteries to run lights, pumps, radar, instruments, etc. These batteries have a shore-powered charger 3 x 10 amps. My shore power plug is 30 amp capacity.
I have an isolated pair of lithium batteries that run the 12v cabin AC, hot water heater, cabin lights, and shower pump. These lithium batteries are charged by solar panels on the cockpit roof. This system worked very well until I added a cover to my boat lift. The charging rate on the lift is greatly reduced.
I wonder if adding a DC to DC charger that would recharge the lithiums from the house batteries would solve this conundrum. As I understand DC to DC chargers, there is no transfer of power until the source batteries are fully charged. Is that correct?

Are you wanting to charge the lithium bank while you’re hooked up to shore power, when you’re disconnected from shore power, or both?

I assume you want this to be able to charge while on shore power or with alternator power if you’re looking at a dc-dc charger

This is exactly what they’re designed for!

The smaller chargers are somewhat limited in features, the 50a is probably a little overkill but has a lot more flexibility

Either way you shouldn’t have an issue setting it up to kick on once the engine is running or the shore power chargers have kicked in.

Thanks for the replies. Yes, charging when on shore power or underway.
I willl look at the 50a version. The 18a doesn’t connect to Cerbo that I can see.