Prima di entrare, lascia gli stivali sullo zerbino.

Because prima di + infinitive is the normal Italian pattern for before doing something.

So:

• prima di entrare = before entering / before coming in
• prima di mangiare = before eating
• prima di uscire = before going out

The di is required here before the infinitive entrare.

Here lascia is the informal singular imperative of lasciare, so it is a command addressed to one person you would say tu to.

• lascia! = leave!
• lasci! = formal singular command
• lasciate! = plural command

So this sentence is speaking casually to one person: Leave your boots on the doormat before coming in.

In Italian, subject pronouns are often omitted because the verb ending already shows who the subject is.

So:

• lascia already tells you it is addressed to tu
• saying tu lascia would usually sound unnecessary or unnatural in normal speech

Italian often leaves out pronouns unless there is emphasis or contrast.

Italian very often uses the definite article where English uses your, especially with clothing, body parts, and personal items when the owner is obvious from context.

So:

• lascia gli stivali literally = leave the boots
• natural English translation = leave your boots

You could say i tuoi stivali, but it would usually add emphasis, as if you are contrasting them with someone else’s boots.

Sullo is the contraction of:

• su = on
• lo = the

So:

• su + lo = sullo

You use lo because zerbino is a masculine singular noun beginning with z, and nouns beginning with z normally take lo:

• lo zerbino
• sullo zerbino

In Italian, masculine singular nouns usually take:

• il before most consonants
• lo before z, s + consonant, ps, gn, x, y

Since zerbino starts with z, it takes lo:

• lo zerbino
• uno zerbino
• sullo zerbino

This is a standard article rule.

It can mean both, depending on context.

In this sentence, prima di entrare is naturally understood as:

• before entering
• before coming in

English often prefers come in in this everyday situation, while Italian simply uses entrare.

Yes. Lasciare is commonly used for leave in the sense of put/keep something somewhere and not take it with you.

So:

• lascia gli stivali sullo zerbino = leave the boots on the doormat

It does not mean leave in the sense of go away here. The context clearly shows it means set them down / keep them there.

The comma separates the introductory phrase Prima di entrare from the main command.

It is similar to English:

• Before coming in, leave your boots on the doormat.

In Italian, this comma is natural and helps readability, though punctuation can sometimes be a little flexible in short sentences.

Yes. Italian allows some flexibility.

For example, you could also say:

• Lascia gli stivali sullo zerbino prima di entrare.

This means essentially the same thing.
The version with Prima di entrare first puts more focus on the before entering part.

Stivali is the plural of stivale.

• lo stivale = the boot
• gli stivali = the boots

Since people normally wear two boots, the plural is the natural choice here.

It is informal, because of the command lascia, which is the tu imperative.

If you wanted to say it formally to one person, you would say:

• Prima di entrare, lasci gli stivali sullo zerbino.

If you wanted to say it to more than one person:

• Prima di entrare, lasciate gli stivali sullo zerbino.