L = the voltage of the battery is dropping to 11.5v under load.
It could indicate that the battery needs replacing. Whenever we have had issues with a failing leisure battery, they have always shown up as fully charged. What happens is the the battery lost its capacity and started to go flat once that reduced capacity was exhausted.
The battery started off as expected but would 'die' a few hours into the work schedule. So a 110 amph leisure battery ended up with a capacity of 20 amph.
From a discharged state we noticed they they very quickly became fully charged.
It could also be a bad connection as has been posted by others. The first place to check is at the fuse holder. If it gets hot then there is a resistance - a resistance causes a current restriction and reduced voltage.