[AmityvilleHams]

Eucalyptus definitely shouldn't be used around/in the same room as small pets in general. It also should be avoided around cats by the way as they can be fairly sensitive to it as well for a variety of reasons, though you shouldn't ever allow cats or other predatory pets(ferrets and dogs for example) to be in the same room as hamsters anyway. It's very strong especially when dealing with the essential oil form and would definitely be capable of irritating delicate hamster respiratory systems.

Food grade diatomaceous earth would be worth considering(just not pool filter grade or any other sort of non food grade type as they're not necessarily going to be free from potentially harmful contaminants/additives/impurities/etc). It kills insects in a way that cannot be adapted against like the synthetic pesticides as it is a mechanically killing type of thing - it has grains that are just sharp enough to pierce exoskeletons which leads to the insects essentially drying out and dying, but it's not actually sharp to hamsters for example or humans.

Keeping lizards out however would be another issue as wild lizards(and many wild animals in general) can harbor & spread things like parasites and disease. Finding and patching holes or sealing them up in some way is the long term goal but it can be difficult to find every little hole. The main thing is preventing them from getting around your hamster or any other pets though. I would definitely find some sort of way to keep the hamster's cage off the ground in this case, preferably at least somewhat away from touching walls too if possible.