Wow what a topic. I love reptiles just as much if not more than plants, no scratch that way more....
In any case basilisk lizards are mainly insectivores and you will never have a problem with them eating your greens down to the trunk. They are really neat and watching them run on there hind legs is so very fun to watch.
O slats and veils Chameleons are another controversial lizard living down here.. I have never seen one but I hear they live down in the avocado groves in homestead. Maybe the growers are trying a more natural approach to insect control?
Now spinytail and green iguanas do regularly eat greens in adult hood. But they are not like squirrels or birds that travel much faster and farther trying multiple fruits at a time
It's a double edge sword though yes they eat leaves and fruit but they also are heavy snail eaters. There was even a report on how many native tree snails they eat.
Freezes do kill off many of the non native wildlife but that is also making a more cold tolerant reptile that will be better equipped for the cold next time a freeze comes down.