תזכירי לי לקחת את הספר ואת המפתח לפני שאני יוצאת.

Yes. תזכירי is formally the 2nd person feminine singular future of להזכיר (to remind).

In everyday Modern Hebrew, though, the future tense is very often used as a command/request, especially in speech. So here תזכירי לי means Remind me when speaking to one woman.

A more textbook-style imperative would be הזכירי לי, but in normal conversation תזכירי לי is usually more natural.

So in this sentence:

• תזכירי = you (female) remind / please remind
• it is directed to a female addressee

Because Hebrew verbs usually already show the subject.

In תזכירי, the ending tells you:

• 2nd person
• feminine
• singular

So Hebrew normally does not need an extra pronoun here.

If you added את (you, feminine singular), it would usually be for emphasis:

• את תזכירי לי = you are the one who should remind me

But in a normal sentence, just תזכירי לי is enough.

לי means to me / for me.

It is made of:

• ל־ = to
• ־י = me

With the verb להזכיר (to remind), Hebrew often uses the person being reminded with ל־:

• להזכיר לי = to remind me
• literally, something like to remind to me

So:

• תזכירי לי = remind me

This is just the normal Hebrew pattern, even though English uses a direct object.

Because לקחת is the infinitive form: to take.

Hebrew commonly uses this structure:

להזכיר למישהו + infinitive
= to remind someone to do something

So:

• תזכירי לי לקחת = remind me to take

This works very much like English:

• Remind me to take...

Other similar examples:

• תזכירי לי להתקשר = Remind me to call
• תזכירי לי לקנות חלב = Remind me to buy milk

Here את is the direct object marker. It does not mean you in this sentence.

Hebrew uses את before a definite direct object. Both nouns here are definite because they have ה־ (the):

• הספר = the book
• המפתח = the key

So:

• לקחת את הספר = to take the book
• לקחת את המפתח = to take the key

This את usually has no English translation. It is just a grammar marker.

A useful contrast:

• לקחת ספר = to take a book (indefinite, no את)
• לקחת את הספר = to take the book (definite, with את)

Because there are two separate definite direct objects:

• the book
• the key

Hebrew very commonly repeats את before each definite noun in a list or pair:

• את הספר ואת המפתח

This is the most natural and clear phrasing.

Also, ואת is just:

• ו־ = and
• את = direct object marker

So:

• ואת המפתח = and the key (with the object marker included)

לפני means before.

When Hebrew wants to say before followed by a full clause, it often uses:

לפני ש־...
= before ...

So:

• לפני שאני יוצאת

contains:

• לפני = before
• שאני = that I / that I am, from ש־ + אני

Very literally, it is something like:

• before that I leave/go out

But in natural English, it is simply:

• before I leave

יוצאת is the feminine singular form of יוצא / יוצאת (going out / leaving).

So it tells you that the speaker is female, because the subject is אני (I):

• אני יוצאת = I am leaving / I leave said by a woman

And earlier in the sentence, תזכירי tells you the person being addressed is also female.

So this sentence is spoken:

• by a woman
• to a woman

If a man were speaking, you would say:

• לפני שאני יוצא

If speaking to a man, you would say:

• תזכיר לי

This is a very common question.

יוצאת is formally a present participle form, but in Modern Hebrew it is often used for a near-future or planned action, especially in everyday speech.

So:

• לפני שאני יוצאת feels natural and conversational: before I leave / before I head out

A more explicitly future version would be:

• לפני שאצא

That also means before I leave.

Very roughly:

• לפני שאני יוצאת = more everyday, immediate, conversational
• לפני שאצא = a bit more explicitly future, sometimes slightly more formal or neutral

Both are good Hebrew.

The forms that change are the ones that show gender.

Original sentence:

• תזכירי לי לקחת את הספר ואת המפתח לפני שאני יוצאת.
• female listener, female speaker

Common variants:

• תזכיר לי לקחת את הספר ואת המפתח לפני שאני יוצא.
  male listener, male speaker

• תזכיר לי לקחת את הספר ואת המפתח לפני שאני יוצאת.
  male listener, female speaker

• תזכירי לי לקחת את הספר ואת המפתח לפני שאני יוצא.
  female listener, male speaker

So:

• תזכירי / תזכיר changes with the person being addressed
• יוצאת / יוצא changes with the speaker

A simple transliteration is:

tazkiri li lakakhat et ha-sefer ve-et ha-mafte'ach lifnei she-ani yotzet

A few pronunciation notes:

• תזכירי = tazkiri
• לקחת = lakakhat (the ח is a throat sound)
• את = et
• ואת = ve-et
• לפני = lifnei
• שאני = she-ani
• יוצאת = yotzet

So you could read the whole thing aloud as:

tazkiri li lakakhat et ha-sefer ve-et ha-mafte'ach lifnei she-ani yotzet