This depends on the electric spec of the lights. Just quickly glancing over the link you provided, it seems this is using E12 light bulb, and I suppose it means it requires 110V powerline voltage, so you can’t directly light it up with OSPi, because OSPi outputs 24V AC which is far below 110V. There are several options
1. use OSPi to drive a relay and use relay to switch the lights. OSPi does have a built-in relay, but that’s only rated 3 Amp contact current, so likely you need an external relay.
2. use OSPi combined with an RF remote power socket to switch powerline devices. I have a blog post about it: http://rayshobby.net/?p=3381 (note that the blog post uses OpenSprinkler as example, but the same functionality can be implemented for OSPi).
3. instead of using 110V light bulb, use 12V LED lights. 12V LED lights can be directly connected to 24V AC output (because LED is intrinsically diode, it blocks half of the AC waves, making the effective voltage 12V).