This is how it works - SOeP is a designated ADR body. LX is a participant in the scheme.

This means that SOeP reconcilliation attempt is mandatory, if there is jurisdiction. SOeP has jurisdiction to do this in Germany and the UK. In such case LX has to attempt reconcilliation.
If the ticket does not touch UK or Germany, SOeP will offer to do the reconcilliation to LX (or any other member airline) and if they accept, they would be bound by the decision. However, LX does not have to accept the attempt.

LX knows it's in their benefit to deny any attempt at reconcilliation and do the bare minimum, since there is no easy way to go after them, unlike in many EU countries where you could use mechanisms like European Small Claims procedure.