Do I just leave it in my inventory and wait for the RE? What does the repellent do? And does it work if I lock the item?

Yes, they work when locked in your inventory. [edit] Sorry, had a customer. The trap and the spray work together to get you the potentially rare item the lizards are making off with. By itself the trap gets you a and an achievement

[edit] got to it first :P

Do you know if I can get the achievement with both, or must I only have the trap itself? Thank you for the answers! Thank you, too!

There's an achievement for taking things from the lizards that you get when you have both items locked in your inventory, and one for trapping the lizards that you get with only the trap. (Pop the repellent in your vault if you're going for the comatose lizard achievement)

Thank you so much!