It's not completely stupid. One pissible issue: when the light level is around the threshold, slight variations (think: cloud passing by) will cause the relay to switch back and forth quickly. This can be solved with some additional parts (keyword: hysteresis).
I would recommend using a microcontroller, it makes this problem easy to solve, plus you can have more logic to trigger the lights (eg time based).
Another thing is turning off: if it's purely based on light level, you need to make sure the sensor does not "see" any of the LED light, otherwise it thinks the sun is back up