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You can probably modify your lead acid charger to output a few more volts, assuming it outputs enough amps in the first place to charge your batteries in time. How hard that is to do depends on your charger. A "dumb" charger with a simple voltage limit cutoff will require figuring out how to change the circuitry to cut off at the correct voltage. An "intelligent" charger, if you're lucky, will have an adjustable potentiometer to easily change the output voltage, within reasonable limits. Either way, you'll want some kind of BMS to protect you lithium batteries from over-charging.
Or you can look for an inverter that runs on a higher voltage and configure your lithium pack to match it. You'd still need a new charger, but seeing as it would be lower amperage, it would be more affordable. Doubt it would cover the cost of a new inverter, though.
The question that comes to mind is...where's the nearest mains outlet that you could plug in to instead?
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