The SMAJ series are not zener diodes. They are TVS: Transient Voltage Suppressor diodes. These are meant to conduct electricity when the voltage on the DC input is beyond a set limit: in your case 15V with the SMAJ15.
What this prevents is spikes of voltage beyond 15V from reaching your lamp. Anything more than 16.7V will trigger a breakdown. If there is too much current or voltage, this will short out and break the fuses on either the board or the power source.
You always want a TVS diode that is slightly higher rated in voltage than your operating voltage, to prevent unneeded suppression.
The 15V SMAJ15 is the ideal TVS diode for your application. I'd check your power supply though, since this doesn't break without a reason.