I think that such a sentence implies that we know what lion we're talking about, it was probably mentioned before. If it was "This is a big lion", with the lion mentioned for the first time, there would be no problem.
"lew" is a masculine noun, so the adjective has to match. "duży" is a masculine form.
"duże" is neuter.
I'm having a very hard time, usually when the man is speaking, hearing the difference between the -y ending and the -e ending. Are the words "duży" and "duże" supposed to sound so similar?
As a native speaker I would never even consider them similar, but I know that this is a problem that a loooot of our students have, so you're not alone. I guess there's no other way than to just listen a lot and hopefully you'll start recognizing them soon.