Learn Arabic (Modern Standard): لم يترك المنقذون الشاطئ.

The negation word لم is used specifically to say that something did not happen in the past. However, grammatically, it must always be followed by a present tense verb in the jussive state. Together, لم يترك means "did not leave".

If لم makes the verb end in a sukoon (no vowel), why is a short "i" sound pronounced at the end of يترك here?

You are right that يترك normally ends with a sukoon after لم. But the next word, المنقذون, starts with a silent consonant sound. Arabic does not allow two silent consonants in a row, so a helper "i" vowel (kasra) is added to the end of the verb to connect them smoothly. It is pronounced "yatruki l-munqidhūna".

Why is the word for lifeguards written as المنقذون instead of المنقذين?

Because the lifeguards are the subject of the sentence (they are the ones doing the action). Regular masculine plural nouns end in ون (-oon) when they are the subject (nominative case), and ين (-een) when they are the object of a verb or follow a preposition.

How is the word المنقذون built from its root?

The root is ن ق ذ (n-q-dh), which relates to saving or rescuing. From the Form IV verb أنقذ (to rescue), we get the active participle منقذ (rescuer or lifeguard). The prefix ال makes it definite ("the"), and the suffix ون makes it plural.