Burst into tears and Let out

Let out and burst into tears are semantically related In some cases you can use "Let out" instead a verb phrase "Burst into tears".

Let out verb - Express audibly; utter sounds (not necessarily words).

Burst into tears and let out are semantically related in cry topic. Sometimes you can use "Burst into tears" instead a verb "Let out", if it concerns topics such as weep and make sad sounds.