Learn French: Notre lieutenant est très jeune. - Our lieutenant is very young.

Because the profession (lieutenant) is modified by an adjective (très jeune), you must use C'est un instead of Il est plus the zero article. The correct sentence would be: C'est un très jeune lieutenant.

If I rewrite this as C'est un très jeune lieutenant, why does jeune go before the noun?

Jeune refers to age, making it one of the short, common adjectives that typically precede the noun. Adding the adverb très does not change this placement rule, so putting it before the profession is perfectly natural.

What if the lieutenant is a woman? Does the word lieutenant change?

Traditionally, military ranks in French remain masculine regardless of the person's gender, so you would still say notre lieutenant. However, the feminized form lieutenante is becoming much more common today, especially in civilian or police contexts.

Do I make a liaison between est and très when saying this sentence out loud?

In everyday spoken French, no. While a liaison after the third-person verb est is grammatically optional, native speakers almost never pronounce the 't' before words like très in casual conversation.