"I have a lot of long pencils."
Translation:У меня много длинных карандашей.
I think because the focus here isn't on the fact that you have long pencils but on the number of long pencils that you have.
"Есть" is emphasizing the existence of an object, rather than a characteristic (such as number). I guess here the fact of interest is not that you have pencils but that you have a lot of them. That said, I wouldn't be confident that "есть" is necessarily wrong here, it's maybe worth reporting just in case.
CJlon, your sentence is perfectly fine! Опять пьяные китайцы постарались ;)