Can I use the message kit with a traditional lead acid battery or power it from AC mains?

Absolutely. The “SLOW DOWN” kit is designed to operate from any DC source ~7.5VDC to 18VDC including traditional 12VDC nominal lead-acid batteries. To operate from AC mains, you need to provide and inexpensive 5 Watts or greater AC to DC converter. Many such converters are available in the market.