Probably. An inverter doesn't know or care what battery type supplies the DC current to invert to AC.
Also, the inverter is a bit flexible with the supplied DC voltage to invert out to AC.
Your DC voltage however is more applicable to the battery charger, some of which are built in to "inverters", some of which are separate devices / chargers. You don't say what you have, just a model name, which is hoping someone knows that exact model and understands your question and has the knowledge to explain more.
However, some appliances might be picky about the type of AC current produced by an inverter, if it is a modified sine wave, vs a pure sine wave, neither of which is relevant to the supplying DC battery types vs the quality AC output by the inverter.
There are also other considerations too but without a lot more specifications about your inverter, it will be up to you to list them or read your user manual.
LOTS of inverter questions have been asked lately and thoroughly discussed in the past, so searching the forums for inverter info will help you immensely to understand the way things work and your inverter, along with the inverter user manual.