There is no such thing as cheap LP. There are only 2 ways to book.
1. pay a cash ticket. Prices are constant. There is no peak or low season. Calculate 5/7k in € for one way and 8/10k for a round trip.
2. hope for an upgrade when flying J. Very risky as you are not in control of there is an upgrade available at all and if so, for which price. That can fluctuate a lot.
DXB is one of the least expensive routes. But also very short.
there is a 3rd way to book and that is with Flying Blue miles. Only possible when you are Platinum or higher. Cheapest destination is IAD for 150.000 miles ex Europe.