The Lucky Mine is a mine located below the lab. It is seen in the Lucky Ores Mod Review.
There is a trail of minecart tracks leading out of the lab and into the Lucky Mine. The entrance is a hole straight down onto another bit of minecraft track.
On the lower level of the mine is a set up of the Ruby Ore, Saphire Ore, and Emerald Ore, each with chests containing their own sets of weapons, tools and armor.