You can trigger the gate of the triac using a latching relay that is rated for a couple A and for the mains voltage.
Just connect MT2 to the gate through the relay contact and a resistor of a few hundred ohms. The relay contact switches very little current on average so it will last a long time.
Make sure the relay isolation is appropriately rated for safety reasons.
Alternately, consider a dual transistor-output optoisolator, a supply derived from the mains to supply the circuit, and either direct drive or a triac driving optoisolator. Control a S-R latch (74HC74 using R and S inputs or a cross-connected gate) with the dual optoisolator.
Pulse the LED of one half the dual and it turns on, pulse the other LED and it turns off.
If the mains power gets interrupted it will lose knowledge of the state. If you want to avoid that, it might be easiest to replace the gate with a microcontroller that has EEPROM, but everything else could remain the same. It's pretty straightforward either way, but a fair number of parts.