When you pronounce the "L" it is pronounced "el". Now go check a grammar guide to see if I was wrong.
If it were "local" it would be "a".
By this rule, if the abbreviation starts with a vowel-sounding letter, the article used is "an"; if it starts with a consonant-sounding letter, it takes an "a". This would give "an NHS hospital" and "a BBC documentary".
I stand corrected. I was always taught to use the entire phrase instead of the abbreviation.
Public schools FTL.

