Step-up power module XL6009 converter and >4Amp power source!
Here is the way to evaluate this. Your LEDs will consume 3.56 watts (17.8 volts * 0.2 amps). The battery must supply this power. But the battery is at 12 volts (perhaps slightly more) so there will be 0.3 amps (3.56 watts / 12 volts) drawn from the battery through the boost converter. And actually it is a little more than that since the boost converter burns up some power as well. If we assume it is 90% efficient then the amps on the battery side will be 0.33 amps (0.3 amps / 0.9).

The battery supplies amps to a load. The less amps drawn, the longer the battery will last before needing recharging. Your battery is rated at 7 Ah.  This is calculated over a 20 hour period for most batteries. This means 0.35 amps for 20 hours (7 Ah / 20 hours). But you will be drawing 0.33 amps. So your battery life will be about 21 hours (7 Ah / 0.33 amps).  

Take care when using a boost converter such as this. Left unattended, it can draw down your battery voltage to the point of damaging the battery. So stop using your LED when the battery voltage drops to 10.8 volts and then start charging the battery. If you would like your battery to support more charge/discharge cycles, bump that limit up to 11.6 volts.