What is Smaug's lineage? Has his ancestry ever been documented?
I always took Glaurung's title as Father of Dragons literally, ie all dragons are his descendants rather than him merely being the first of his kind created by Morgoth.
So Tolkien makes reference to Melkor "breeding" dragons, Glaurung being the father of dragons. And at the fall of Gondolin Morgoth having a host of dragons, many and terrible. Then during the war of wrath came winged dragons of which many were slain but others escaped.
After the first age the dragons continued to breed and repopulate in the northern waste.
Then in the third age they began to harass men and dwarves and made war with them.
Perhaps a family tree with dragons would have been far too much to ask for, but one can always dream.
No, but Smaug is a winged fire-drake which traces his lineage to at least the winged dragons of the Great Battle (the War of Wrath) and possibly back to Glaurung himself.