Electronic – Solid State Relay replacement for SRD-12VDC-SL-C

SSRs use triacs as switching elements, and those are for AC, not DC. A triac is like two transistors so arranged that, once ignited, they keep each other switched on. The only way to switch it off is to reduce the current to below the hold current. AC devices do this 100 or 120 times per second, at zero crossings of the mains, but at DC it will not switch off.

Instead of interrupting the circuit you can also briefly short-circuit the triac's terminals to switch it off.

This sounds like a good application for regular old mechanical relays. They won't care about the direction of current, won't have a offset voltage, and their off leakage is zero in a practical sense.

Relays that can switch house power are common and available in a variety of coil voltages. Since you say you want to switch "lights", it seems like the current will be low. Relays that can do this will be small and available in coils meant to be driven from 5 V. This means you can run them from the same power supply as the processor doing the controlling, but not that the relays can be run directly from a digital output. You will need a transistor controlled by the digital output that in turn controls the larger relay coil current. Don't forget the reverse diode accross the relay coil, else you'll end up with fried transistors.