L-theanine completely destroys my ability to sleep. I've tested a few times now. Dosage used was 100mg, taken early in the day. It's like I get stuck in super light sleep where I'm practically dreaming but awake.
Green tea does have caffeine, so I'm not sure if your side effects are related to L-theanine. I also have trouble sleeping as well when I have afternoon caffeine. I don't feel awake, but I just cannot sleep. It took a while for me to associate this with late caffeine.