Actually, consider this.
A box has around 2 LVX's. And 1 Shiny (Average)
So.
2 out of the 5 LVX's are found in one box. That means that on average, after 3 boxes you have each LVX one time, and one more copy of one of the 5.
1 out of the 3 Shiny's are found in one box. That means that on average, after 3 boxes you have one copy of each Shiny, and no more spares.
So actually, a Shiny is MORE RARE then a LVX is.