According to multiple sources I have read, the odds aren't known, but they are estimated to be around 5%.
Source: https://pokemongohub.net/post/news/2020-lunar-new-year-lucky-trade-odds-are-around-9-now/
However, quick note. There was an article published a little over a year ago that contains some interesting data. Apparently, when a trade is conducted, it looks at the age of the oldest Pokémon being traded. If it is less than a year old, it has an 5% chance of being a lucky trade. A year to 2 years is 10%, 2 years to the August 2016 is 25 Percent. Finally, any Pokémon caught between July and August 2016 have a 75% chance of becoming a Lucky Trade. Also, if you have less than 10 Lucky Trades, it is guaranteed to get a Lucky Trade if you meet the 75% odds. However, this was in 2019, so it may have changed, but I doubt it.
Source: https://thesilphroad.com/science/chance-of-lucky-trade/
Hope this helps!
