This is a question that I have had for years. I have always heard that it was Latin, but I decided to check it out. I found this answer, which is pretty interesting. I will *ahem* abbreviate his answer here.
Lb is short for libra, which is short for libra pondo, which is Latin for "pound weight." You may recognize that the zodiac symbol for Libra is a scale, which is a reference to weighing and measuring things.
The British currency of pounds uses an abbreviation of libra pondo, too. Have you ever realized that the symbol for British pounds (£) is actually just an ornate "L"? That's because it is short for libra pondo. The connection between weight and currency is this: back in the day, one pound of silver was worth one pound.
But I didn't stop there. I was hooked. I kept looking up abbreviations that I didn't understand. Why, for instance, was "number" abbreviated "no." even though there isn't an "o" in the word? It turns out that it's from the Latin word nomerei.
Then I wondered why we abbreviate "pages" as "pp." instead of "pgs." or something else that made sense. It turns out that it's just a style convention. I don't think there is any real reason. The article on abbreviations on Wikipedia is kind of interesting. Did you know that P. is the official abbreviation for "pope" and PP. is abbreviated for "popes"? I had know idea that the pope had his own abbreviation.