Hi Melanie,
If this is going to be under a metal grate, then it is probably OK. If there is no grate, this type paper can trigger hormones and your bird will want to make a nest out of it. If your bird is a female, this can make her lay eggs. Also if your bird can reach the paper, not all inks are safe. A good option is unprinted newspaper or packing paper, and you can find that at office supplies or Amazon.
Lavender is safe as long as it is organic and has been grown in soil that hasn’t been treated with anything. As far as having it in the cage all the time, only if the bird can’t reach it. Otherwise if the bird can eat it, he might eat more than is safe and get sick or worse. If you mean the oil, this is highly concentrated and only a small amount should be use around a bird.
Thank you for Asking Lafeber,
Brenda