your birdcage probably has drainage holes at the bottom rails. I plugged these with rubber stoppers. Also, the are small expansion joints in the concrete pad which connect to the outside as wall. I taped these over on the outside. No critters since

Anoles etc...
 

Sticky traps catch and hold many critters. Check daily because a stuck Anole can be freed outside by putting olive/coconut oil on them. They'll wiggle and tug to free themselves in short order, and, have beautiful skin.

Gaps
 

We were getting small ones in our enclosed lanai and figured out they were sneaking through the small gaps at the bottom where the sliders meet. Does not take much space.

I blocked the gap with a removable rubber piece and have not had any since.

moth balls around outside

Giggle, snort, only problem I have is my dachshund likes to mangle the little creatures which is worse than the poop.

Caulking will solve the problem

Great answer. I wondered how big wasps, anoles, crickets got in the lanai. I'll check on blocking the outside siding holes.

If you spray pesticide around your foundation and landscape pieces and from the inside out spray home defense on hour screens every few weeks they'll have nothing to eat and will mosey on over to the neighbors house. Our biggest problem are those baby frogs that come around a couple times a year climbing up and down our windows on the outside.

I love my little anole. He lives in the door threshold. I feed him 2-3 small crickets a day from PetSmart. I will shake the bag and he knows it’s lunch time. The males ( which I have) are territorial so you will only have one male there. When he wasn’t around for a few days I missed the little guy but then all of a sudden his head popped out! PLEASE do not use sticky traps, such a cruel way to die. They are a part of the fun of living in Florida!

They are Anoles. In our lanai, they do us a great service by keeping bugs down. Their poop is a minor inconvenience.

They are not hurting anything, especially your new furniture. Catch and release if you must but don't hurt the little criters

yeah, someone with common sense..

You may want to try an ultrasonic pest repeller. Google says: "They can be effective but must be used wisely. Place them in a room where there is lizard activity and make sure not to position them behind furniture, which can block the signal. Keep in mind that they will only work for one room, as the ultrasonic sound cannot penetrate walls."

OP stated “enclosed lanai “ not birdcage