Can the lock be saved?

Usually. Extraction is routine work. The lock gets replaced when it was already worn out, which is often what caused the break in the first place.

Half the key is still in my hand.

Keep it. It makes cutting a replacement much easier and it proves the whole key is accounted for.

Then the lock needs servicing or replacing, not just the key. Fitting a new key to a seized lock buys you another broken key.

Stop using the door

A snapped key can normally be extracted and the lock kept. What ruins it is what people do in the next five minutes.

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Do not push the broken piece further in. That is what turns a five-minute extraction into a replaced lock.
Do not try to grab it with pliers unless it is genuinely sticking out — you will usually break it flush.
Do not use superglue on the other half of the key. It is a real thing people try and it glues the lock solid.
If the lock was stiff for weeks before this, say so. It matters for the repair.

The broken piece extracted with proper tools rather than dug at.
The lock checked for what made it break — usually it was stiff long before it snapped.
Lubrication and servicing, or a new cylinder if it is worn out.
A fresh key cut from the original where one exists, rather than a copy of a copy.
Rekeying if part of the key is missing and unaccounted for.

Can the lock be saved?: Usually. Extraction is routine work. The lock gets replaced when it was already worn out, which is often what caused the break in the first place.
Half the key is still in my hand.: Keep it. It makes cutting a replacement much easier and it proves the whole key is accounted for.
It broke because the lock is stiff.: Then the lock needs servicing or replacing, not just the key. Fitting a new key to a seized lock buys you another broken key.

Free estimate. The price is agreed before the work starts.

One Call Locksmiths arranges the visit; the technician does the work and gives you the price.