Verkstaden hade ingen reservdel i dag, men kvinnan där sa att de kan laga cykeln i morgon.

Verkstaden is the definite form, meaning the workshop / the repair shop.

• en verkstad = a workshop / a repair shop
• verkstaden = the workshop / the repair shop

Swedish usually adds the definite ending to the noun itself, instead of using a separate word like the.

Here, verkstad means a repair shop or workshop, probably a bike repair shop in this context.

Depending on context, verkstad can also mean a general workshop, garage, or place where things are repaired or made.

Hade is the past tense of ha (to have).

• har = has / have
• hade = had

So Verkstaden hade ingen reservdel i dag means the shop did not have a spare part today.

Ingen is the normal Swedish word for no / not any with a singular en-word noun.

• ingen reservdel = no spare part
• inget is used with ett-words
• inga is used with plurals

Examples:

• ingen cykel = no bicycle
• inget problem = no problem
• inga reservdelar = no spare parts

Using inte en reservdel would sound much less natural here.

Because the sentence says the shop did not have a spare part / any spare part available, using a singular noun after ingen.

If the idea were specifically plural, Swedish would say:

• inga reservdelar = no spare parts

Both are possible in principle, but ingen reservdel is a very natural way to express that there was no suitable spare part.

These expressions mean:

• i dag = today
• i morgon = tomorrow

Literally, i often corresponds to in/on/at, but in these time expressions you should just learn them as fixed phrases.

You will also often see the spellings:

• idag
• imorgon

Both spellings are commonly accepted in modern Swedish.

Kvinnan där means the woman there. It identifies which woman is being talked about: the woman at that place, probably at the repair shop.

Swedish often uses this kind of structure when introducing or specifying someone:

• mannen där
• tjejen där
• kvinnan där

If the person had already been clearly established in the conversation, hon (she) could also be possible, but kvinnan där gives more identification.

Here där means there and works like a location marker: the woman there.

It helps connect the woman to the place just mentioned, the workshop.

So:

• kvinnan där = the woman there
• in context: the woman there at the shop

It is a natural but slightly loose, conversational way to identify someone.

This is a very common question for English speakers.

In English, reported speech often shifts the tense back:

• She said they can repair it tomorrow often becomes
• She said they could repair it tomorrow

Swedish does this less strictly. If the information is still valid at the time of speaking, Swedish often keeps the present:

• sa att de kan laga cykeln i morgon

This means something like:

• said that they can repair the bike tomorrow

You could sometimes hear kunde in other contexts, but kan is very natural here because it describes a still-current possibility for tomorrow.

De here means they, referring to the people at the workshop—the staff, mechanics, or the business as a whole.

This is very natural in Swedish. A shop, company, or office is often referred to as de when meaning the people there.

In everyday speech, de is usually pronounced dom.

After att (that / to, depending on context), Swedish uses subordinate clause word order.

Here the structure is:

• att = that
• de = subject
• kan = verb
• laga = infinitive
• cykeln = object
• i morgon = time expression

So:

• att de kan laga cykeln i morgon

Unlike main clauses, there is no inversion here. Compare:

• Main clause: I morgon kan de laga cykeln.
• Subordinate clause: ... att de kan laga cykeln i morgon.

Cykeln is the definite form: the bike.

It is definite because it refers to a specific bicycle already known in the situation—the bicycle that needs repairing.

• en cykel = a bike
• cykeln = the bike

Since both speaker and listener know which bike is being discussed, Swedish uses the definite form.

Here laga means repair or fix.

• laga cykeln = repair/fix the bike

It is a very common Swedish verb for repairing things:

• laga bilen = repair the car
• laga telefonen = fix the phone

You may also see reparera, which is a bit more formal or technical in some contexts.

Yes, it is natural and understandable Swedish.

A few small variations might also be common, for example:

• Verkstaden hade ingen reservdel idag, men kvinnan där sa att de kan laga cykeln imorgon.
• På verkstaden hade de ingen reservdel i dag, men kvinnan där sa att de kan laga cykeln i morgon.

The original sentence is perfectly fine, and the main things for a learner to notice are the definite forms, the use of ingen, and the tense choice in sa att de kan.