Are there more dragons in Gringotts that protect vaults just like the Lestrange's? Or is it just the Lestrange's with dragon protection?
Well that dragon wasn't only there for the Lestranges' vault.
A gigantic dragon was tethered to the ground in front of them, barring access to four or five of the deepest vaults in the place.
Harry Potter and the Deathly Hallows - p.432 - Bloomsbury - Chapter 26, Gringotts
Whether the other deep vaults are protected in exactly the same way I'm not sure, but it seems that some unspecified number of deep vaults are similarly well-protected.
'I have visited the Lestranges' vault only once,' Griphook told them, 'on the occasion I was told to place inside it the false sword. It is one of the most ancient chambers. The oldest wizarding families store their treasures at the deepest level, where the vaults are largest and best protected ...'
Harry Potter and the Deathly Hallows - p.411 - Bloomsbury - Chapter 25, Shell Cottage
Whether the Lestranges' vault, and the other three or four guarded by the dragon, are the best protected or not is not said. Whether there's only one dragon in Gringotts is not clear, but it's certainly true that there are a number of well-protected vaults. Is it more than these four or five? Probably.
Also, Hagrid, at least, reckons there's more than one dragon, but this is slightly weak evidence:
'Why would you be mad to try and rob Gringotts?' Harry asked.
'Spells - enchantments,' said Hagrid, unfolding his newspaper as he spoke. 'They say there's dragons guardin' the high-security vaults. [...]'
Harry Potter and the Philosopher's Stone - p.51 - Bloomsbury - Chapter 5, Diagon Alley
And, of course, no dragon is passed on the way to vault 713.