You're both right. She is probably reading it in her head as, "Louis Vuitton," while you are reading it as, "El Vee." A Louis Vuitton, an el vee.
You use "an" before a vowel SOUND. When you say the name of the letter "L", it's pronounced "ell," which starts with a vowel sound. So you use "an" before it. But you wouldn't use "an" with EVERY abbreviation. Suppose you were watching an animal documentary from the World Wildlife Fund. You'd be watching "a WWF documentary," because the name of the letter "W" is "double-u," which starts with a consonant sound (a "d" sound), which takes "a" not "an" before it.
Pretty sure you were correct, since you abbreviated it.
We Use 'An' before any abbreviation...I want an LV backpack...is absolutely right..."I use to have a Louis Vuitton backpack too" would also be right