So,
Lucky Pokemon have been released - if you've opened your game you'd have seen this notification by now as they've been live for a little over 12 hours if I'm not mistaken. I've compiled a list of known information so far:
1) Lucky Pokémon have a halved Stardust cost to power up, making them reach higher levels at a lower investment. They are easy to identify due to their unique background, green text that says "Lucky Pokémon", and the aforementioned Stardust cost.
2) Lucky Pokémon have an IV Floor of 10/10/10, regardless of your friendship status. This means that if you manage to obtain a Lucky Pokémon, the Pokémon's IVs will be at minimum 10/10/10 and go up to 15/15/15, similar to Eggs, Raid Bosses, and Field Research Pokémon.
3) The older the Pokémon is, the higher the chance of it turning into a Lucky Pokémon. It is not known yet what these percentages are.
4) From what I can tell, if a player receives a Lucky Pokémon, the other player on the receiving end will also guaranteed receive one.
5) There seems to be a cap for Lucky Pokémon, at 10 per day. The specifics are not particularly known other than there seems to be no limit as to what turns Lucky, from Pidgey to Mewtwo.
6) Lucky Pokémon count is tracked in the PokeDex.
Additionally, Gifts now give Stardust and players can receive EXP for sending Gifts.