Every Digimon has a 'luck' stat. This stat increases the chance that you receive random luck drops at the end of a fight. This is particularly useful when you are trying to farm those hard to get MEGA-Digifuels.
Go to the 'enhance' feature in your Digivice's training menu. Here you can upgrade your Digimon's Luck stat.
In this interface you can choose your base Digimon (the one you want to upgrade) and the Digimons you are going to sacrifice to do so.
The Digimon you use to upgrade your base Digimon will be gone forever so make sure they do not have valuable skills or medals!
For a chance for luck to go up the sacrificial Digimon MUST be the same attribute as the base Digimon. Otherwise, your Digimon will only get some EXP.
IMPORTANT: There is no guarantee that your luck will go up. Read more below.
Every Digimon you sacrifice only has a chance to increase luck by 1. This is based on what stage the Digimon you are sacrificing are in. Keep in mind that your Digimon has a luck stats maximum based on its awakening! Also, the odds of increasing luck do not stack.
Example: Champion + Ultimate does not make 100%, rather 1 time a 20% chance and one time a 50% chance.
Rookie : 7%
Champion : 20%
Ultimate : 50%
Mega : 100%
Note: The odds above were found in the game's code but the actual upgrades are done server-sided. However, there is supporting evidence that the odds above are accurate thanks to Reddit user Chortos-2's research.
It is recommended to upgrade luck during events where the chance is doubled. These come around every so often and it is very easy to see when the boost is active.