啦 is a fused contraction of 了 + 啊. It carries the changed-state / completed meaning of 了 plus the softening exclamatory tone of 啊. Colloquial, very common in spoken Chinese.
usage
好啦好啦 is the standard way to placate or dismiss — "okay okay, enough". The 1st-tone reading 啦 is a completely different word — onomatopoeia and a dialect verb meaning "to chat" — and lives on its own page.
Left indexing mouth radical — flags 啦 as a spoken-sound particle. The 口 radical marks the family of fused sentence-final particles: 啦 (了 + 啊), 喽, 嘛 — all tagged "said aloud".
Right 拉 supplies the sound: lā loses tone to become toneless la as a particle. Pure phonetic borrowing — the "pull" meaning of 拉 contributes nothing semantic. 啦 is a phonetic spelling of the 了 + 啊 fusion written with this convenient sound-borrowing.
