As I understand it, auslauts are written whenever a suffix starting with a vowel is attached to a form ending in a consonant. In other words, you would indeed write lugal-le and lugal-la. This isn't a hard-and-fast rule, and there's some variation by time, place, and individual preference (e.g. both tuš-a and tuš-ša₄ are attested), but I don't think it's ever wrong to include the auslaut, and it appears more often than not.
The reason for this, according to Foxvog, is a phonological process that deleted most consonants in final position (or maybe coda position). In other words, aŋrig "steward" represented something like
[aŋ.ri], while aŋrig-ga "of a steward" represented
[aŋ.ri.ga]. Since the basic unit of cuneiform was the syllable, rather than the phoneme, it made sense to write the final syllable as ga rather than a, even though the
/g/ properly belonged to the previous morpheme. (Likewise, aŋrig-ga-ka "in [something] of a steward" would have been
The exceptions, then, generally involve phonemes that weren't deleted in final position, such as š—the sign tuš ("sit") mentioned above, for example, never seems to have been pronounced
/tu/. But regularization is a powerful force, and the spelling tuš-ša₄ doesn't seem to have ever been considered incorrect, even if it never lost its final consonant.
Further reading: CDLI transliteration conventions, Foxvog's grammar