There are 2 ways to increase you "chances" of getting a Lucky Egg:
Maximize the probability of seeing chansey
and
Maximize the probability of catching chansey
1. Improve from 4% to 5.3% encounter rate.
Chanseys spawn at level 26 at 4% in Zone 2. Enter the grass in zone 2 with a level 26 lead and use a repel. This will eliminate encounters from level 23 paras (15%) and level 25 exeggcute (10%). Therefore, chansey's encounter rate will improve from 4/100 (4%) to 4/75 (5.3%).
Tip 1. I recommend putting a single level 26 (surfing) Pokemon in you lead. Preferably staryu with illuminate to increase encounters. You can use surf to quickly enter Zone 2, and a single member will enable you to instantly check the chansey you catch. Tip 2. Instead of using up all your repels, toggle left and right to make encounters without taking a step. Tip 3. Trade over a white flute if possible to your game. This will increase the odds of any encounter (saves the number of left/right toggles you need to perform).
2. Improve catch rate from 10.3% to 19.1%.
A recent video by Professor Rex explains how the mechanics of bait, rock, and balls work in FR/LG. TL/DR: using 2 bait both improves chansey's catch rate and reduces the flee rate. A table of the best decisions to make is found here. If you have all 30 balls, each chansey encounter improves from 10.3% with only throwing balls, to 19.1% if you use bait, then balls. With this strategy, I would say I averaged catching about 2 chansey per safari zone trip.
So what are the odds?
The odds of receiving the lucky egg for every encounter becomes:
(encounter probability)x(lucky egg probability)x(catch probability)
(0.053)x(0.05)x(0.191) = 0.05%
The odds of receiving the lucky egg for every chansey encounter becomes:
(lucky egg probability)x(catch probability)
(0.05)x(0.191) = 0.95%
Therefore, on average you will need to encounter 72 chansey ((99.05/100)^72 = 0.5) before you catch one with a lucky egg. I'm not sure how many I saw, but I got the lucky egg after catching 6. This was a bit fortunate, as a lucky egg per 6 chansey is only around 26.5% to happen. It took around 5 hours.
Best wishes