Within this
Manual I did not see anything relating to battery type also. You should check your Gen Manual to see if the Gen has a adjustment for different type batteries.
Your control can adjust high and low charge rates for low battery charging.
Your new batteries should be fully charged before install by a battery charger.
The generator will take to long to bring them up to full charge and a shore line will keep them topped off so Gen isn't starting and stopping so often.
Once batteries are fully charged you will set the high and low to keep batteries topped off when not on shore power.
The Gen needs house batteries to start which may be drawing to much from the low battery levels so than senses low battery and shuts down.