Jo lenger leieforholdet varer, jo mer betaler kunden.

It is the standard way to express a correlative comparative in Norwegian: the more ..., the more ... / the longer ..., the more ....

So:

Jo lenger leieforholdet varer, jo mer betaler kunden.

means:

The longer the rental agreement lasts, the more the customer pays.

A useful pattern is:

Jo + comparative + clause, jo + comparative + clause

Examples:

• Jo eldre han blir, jo klokere blir han. = The older he gets, the wiser he becomes.
• Jo mer du øver, jo bedre blir du. = The more you practice, the better you get.

Both lenger and lengre can be used as the comparative of lang in many contexts, and in modern Norwegian both are common. However, there is a tendency for:

• lenger to be used more often about time or distance in a general adverbial sense
• lengre to be used more often as an adjective before nouns

In this sentence, varer refers to duration, so lenger sounds very natural:

• Jo lenger leieforholdet varer ... = The longer the rental relationship/agreement lasts ...

That said, learners will sometimes see jo lengre ... too, depending on style and dialect.

Leieforholdet is a noun meaning something like the rental arrangement, the tenancy, or the lease relationship.

It is built from:

• leie = rent / hire / lease
• forhold = relationship / arrangement / condition
• -et = the definite ending for a neuter noun

So:

• et leieforhold = a rental agreement / tenancy
• leieforholdet = the rental agreement / the tenancy

In this sentence, it refers to the rental arrangement already known from context.

Norwegian often uses the definite form where English might say the or where the noun is understood from context.

Here, leieforholdet means the rental agreement/tenancy, not just any rental agreement in general. The speaker is talking about a specific type of situation or a known arrangement.

Compare:

• et leieforhold = a rental agreement
• leieforholdet = the rental agreement

This is normal Norwegian noun grammar: instead of a separate word like the, Norwegian usually adds definiteness to the end of the noun.

Because Norwegian follows the V2 rule in main clauses: the finite verb usually comes in the second position.

In the second part:

jo mer betaler kunden

the phrase jo mer comes first, so the verb betaler must come next, before the subject kunden.

Structure:

• jo mer = fronted element
• betaler = finite verb
• kunden = subject

This is very typical Norwegian word order.

Compare:

• Kunden betaler mer. = The customer pays more.
• Jo mer betaler kunden. = after fronting jo mer, the verb comes before the subject.

So the inversion is grammatical and expected.

Yes. In this sentence, varer means lasts / continues for a period of time.

The infinitive is å vare:

• Møtet varer lenge. = The meeting lasts a long time.
• Leieforholdet varer i ett år. = The tenancy lasts for one year.

So:

• Jo lenger leieforholdet varer ... = The longer the tenancy lasts ...

Do not confuse this with varer meaning goods/products. That is a different word:

• varer = goods, wares

Same spelling, different meaning.

In modern Norwegian Bokmål, the normal comparative form of mye is mer.

So:

• mye = much
• mer = more
• mest = most

Examples:

• Han jobber mye. = He works a lot.
• Han jobber mer nå. = He works more now.
• Han jobber mest av alle. = He works the most of all.

Mere is old-fashioned or literary in Bokmål and is not the usual everyday choice. So jo mer is the standard form.

Yes, that is a very natural interpretation in English, depending on context.

The Norwegian sentence literally says:

the longer the rental agreement lasts, the more the customer pays

But in real usage, English may prefer:

• the longer the lease runs, the more the customer pays
• the longer the rental period lasts, the more the customer has to pay

So the exact English wording can vary a bit, even though the Norwegian structure stays the same.

Yes. This is a very productive pattern in Norwegian.

Some common examples:

• Jo mer, jo bedre. = The more, the better.
• Jo før, jo heller. = The sooner, the better.
• Jo mindre du sier, jo bedre er det. = The less you say, the better it is.
• Jo vanskeligere oppgaven er, jo mer lærer du. = The more difficult the task is, the more you learn.

So this sentence is a very useful model for making similar comparisons.

A few small things may help:

• jo is pronounced roughly like yoo with a Norwegian j sound, similar to English y
• lenger has a clear ng sound
• leieforholdet is a compound, so it helps to hear the parts: leie + forhold + et
• kunden has the definite ending -en, so it means the customer

The rhythm of the sentence often places emphasis on the comparatives:

• Jo LENGER leieforholdet VARER, jo MER betaler KUNDEN.

That makes the comparison especially clear.