In the first movie, when Mr. Tumnus is playing music and Lucy falls asleep, In the flames, was the lion roaring Aslan protecting her and convicting Tumnus?

In this case, I believe first impressions are more accurate than later ones. I think it WAS Aslan the Lion roaring from the flames.

That said, this image was not included in the original book. Rather, in the C.S Lewis story, Tumnus was playing his pipe to (eventually) lull Lucy to sleep. But then she awoke - and this was because Tumnus had stopped playing. She found he was crying. She gives him her handkerchief and tries to find out why he is unhappy. He says "I'm crying because I'm such a bad faun." Then he tells her that he is in the pay of the White Witch. "My father - that's his picture on the wall - he would never have done what I've done," says Tumnus.

In Lewis' story, Tumnus acts from some inner conviction - an awakening conscience that Lucy's innocence AND his father's portrait have stirred in him. (Also, Tumnus in the book DOES believe in Aslan- Tumnus only despairs as to when Aslan will return to free Narnia. But there's something in Tumnus that believes in Aslan the Lion even though Tumnus is, at this stage, still working for the White Witch).

To me, this is MORE dramatic that 'a lion roaring out of the flames'- because in the book Tumnus is feeling an INNER CONVICTION against working for the Witch. In the movie, well who wouldn't be scared if they saw a lion in the flames? But being scared into not doing something is different from realising, right in your heart, that you never ought to have done it in the first place.

So - lion in the flames is Aslan? Yes. And perhaps its just a 'Hollywood' way showing things, but it lacks the conviction embodied by the scene in Lewis' book.

yes yes YES

I think it was, yes. That's not how that scene went in the book, of course, but it's only natural they'd have to change SOME things. The book isn't a screenplay, after all.

Mr Tumnus was protecting her from the White Witch