Vocalic l is the ninth letter of the varnamala, an l that carries a syllable of its own in exactly the way vocalic r does, and it is among the rarest sounds in the language. Grammars introduce it by naming the single verbal root on which its occurrences are built, a root meaning to be fit, to be in order or to arrange, because there is very little else to point at.
The Sanskrit phoneticians class it as dental, grouping it with the sounds made with the tongue at the teeth, and the script gives it a vowel sign written beneath the consonant. That a sound of this rarity has a letter of its own, a place in the canonical order and a vowel sign in the script tells you what the varnamala was built to do. Its authors were not cataloguing the signs a scribe needed but analysing the sound system of the language, and having established that a liquid consonant can function as a syllable nucleus they recorded every liquid that can, regardless of how much use the language made of the possibility. The same logic produced the long vocalic r before it and the long vocalic l after it.
Panini names the sound in the Shivasutras alongside the other vowels, so the rules of the Ashtadhyayi that operate on classes of vowels include it, and the abbreviations that make those rules short are built from a list in which it appears. The Unicode Standard encodes it, and Devanagari fonts provide it, for the same reason the grammarians did: the system requires the place even where the language leaves it nearly empty.