If the artifact creature already has sunburst (or if you control multiple copies of Lux Artillery), each instance of sunburst works separately.

Lux Artillery's last ability will check if there are thirty or more counters among artifacts and creatures you control as your end step begins. If there aren't, the ability won't trigger at all. If there are, the ability will check again as it tries to resolve. If the number of counters among artifacts and creatures you control has fallen below thirty, the ability won't do anything.