Na biurku leży lista zakupów i lista rzeczy do zrobienia przed wyjazdem.

Because Polish often uses a position verb for physical objects.

• leżeć = to lie, to be lying
• stać = to stand
• wisieć = to hang

A list is thought of as something lying flat on a desk, so leży is very natural.

• Na biurku leży lista. = The list is lying on the desk.
• Na biurku jest lista. = There is a list on the desk.

The version with jest is possible, but leży sounds more specific and natural for an object resting on a surface.

This is a very common thing in Polish when the verb comes before a compound subject.

In a sentence like this, Polish often uses singular agreement because the speaker is first presenting what is on the desk, and the subject comes afterward:

• Na biurku leży lista zakupów i lista rzeczy do zrobienia...

This is natural and idiomatic.

You may also hear the plural:

• Na biurku leżą lista zakupów i lista rzeczy do zrobienia...

That is also understandable, and it emphasizes both items together a bit more.

If the subject comes first, plural is usually more expected:

• Lista zakupów i lista rzeczy do zrobienia przed wyjazdem leżą na biurku.

Because na can take different cases depending on meaning.

Here it means location: on the desk.
So Polish uses the locative:

• na biurku = on the desk

If there were movement onto the desk, Polish would use the accusative:

• Położyłem listę na biurko. = I put the list onto the desk.

So the contrast is:

• na biurku = on the desk, already there
• na biurko = onto the desk, movement toward it

It is the locative singular of biurko.

• nominative: biurko
• locative: biurku

It appears here because the preposition na with a location meaning requires the locative:

• na biurku
• na stole
• na krześle

Zakupów is in the genitive plural.

After nouns like lista very often Polish uses the genitive to mean of ...:

• lista zakupów = list of purchases / shopping list
• lista gości = guest list
• lista pytań = list of questions

So grammatically:

• lista = list
• zakupów = of purchases / shopping items

This is a very common noun + genitive pattern in Polish.

Do zrobienia literally means to do or more precisely for doing / to be done.

This is a very common Polish pattern:

• coś do zrobienia = something to do
• książka do przeczytania = a book to read
• pranie do zrobienia = laundry to do

So:

• lista rzeczy = list of things
• do zrobienia = to do / to be done

Together:

• lista rzeczy do zrobienia = list of things to do

In everyday English, this is basically a to-do list.

It comes from the verbal noun zrobienie = doing / making / completing.

After the preposition do, Polish uses the genitive, so:

• nominative: zrobienie
• genitive: zrobienia

That is why the phrase is:

• do zrobienia

This pattern is very productive in Polish and worth learning as a chunk.

Wyjazdem is the instrumental singular of wyjazd.

The preposition przed meaning before takes the instrumental in expressions like this:

• przed wyjazdem = before the departure / before leaving
• przed obiadem = before dinner
• przed egzaminem = before the exam

So:

• wyjazd = departure, trip away, leaving
• wyjazdem = instrumental form after przed

It can mean all of those depending on context.

In this sentence, przed wyjazdem most naturally means:

• before leaving
• before the trip
• before departure

The noun wyjazd often refers to going away somewhere, especially for a trip, holiday, work trip, etc.

Yes, it is very normal.

Polish word order is flexible, and this sentence starts with the location because that is the information frame:

• Na biurku = on the desk
• then leży... = there lies / there is
• then the things being mentioned

This structure is very natural when introducing what is somewhere:

• Na stole stoi kubek.
• Na ścianie wisi obraz.
• Na biurku leży lista...

It feels a bit like: On the desk, there is...

Yes. That is also correct.

That version puts the subject first and sounds more like a straightforward statement about the two lists:

• Lista zakupów i lista rzeczy do zrobienia przed wyjazdem leżą na biurku.

Compared with the original:

• Na biurku leży lista zakupów i lista rzeczy do zrobienia przed wyjazdem.

The original sounds a bit more natural if you are first drawing attention to the desk and then saying what is there.

Because Polish does not have articles like English a/an and the.

So lista can mean:

• a list
• the list

The exact meaning depends on context.

That is why the Polish sentence can be translated in different natural ways depending on the situation.