Usage of lapse referring to a loan application?

I wonder, if a loan applicant chooses not to accept or go any further with a loan application, would you describe that act as cancelling or lapsing the application?, i.e., is the application cancelled or lapsed?

To emphasise: This is specifically related to loan applications, and in Norwegian we use the expression "bortfalle", which literally means "fall away", to refer to both the passive and the active case when it comes to loan applications. The verb usually is a "timeout lapse" in other uses. Are you positive to "lapse" cannot be used transitively in this particular context in English? Would "withdraw" be the financially correct term to use here?

Lapse as a verb is mainly intransitive and means:

• (intransitive] (of a contract, an agreement, etc.) to be no longer valid because the period of time that it lasts has come to an end
  • She had allowed her membership to lapse.
  • The treaty lapsed in 1995.
  • The booking will automatically lapse if the deposit is not paid within two weeks.

• You would cancel the application if you didn't want the loan, or the application might lapse if it had a validity term.

(OLD)

Regarding your edit, withdraw is a correct verb to use:

• To remove from consideration or participation: withdrew her application; withdrew his son from the race.

(AHD)

Regarding the verb "lapse", it is well-explained by other answers.

However, I would use "withdraw" instead of "cancel" when you want to stop the process of the loan application. "Withdraw" means:

Discontinue or no longer provide (something previously supplied or offered):

[Oxford Online Dictionary]

to take (something) back so that it is no longer available

[Merriam-Webster]

You submit the application to get a loan, and withdraw it so that it can be no longer available to and pursued by the bank.

The below Ngram Viewer shows big difference in their usages:

The verb "cancel" works better with mutually-agreed-upon contracts, agreements, and so on. You rarely use "withdraw" for them.

If you simply stop pursuing the loan, then you are allowing the application to lapse.

You would never say that you are lapsing the application. That would imply a positive action but you are simply ceasing its pursuit. Lapsing occurs through inactivity.

However, if you actively inform the lender that you will proceed no further, then you have cancelled your application. That is a positive action.

You could use “abandon” as a transitive alternative to trying to use “lapse” transitively (and awkwardly, at best, as mentioned elsewhere) in this situation; especially if you want to emphasize, for whatever reason, the notion of having taken no [further] action (as opposed to having expressly acted to “cancel” or “withdraw” the application).

In addition to avoiding the notion of having expressly cancelled/withdrawn the application, “abandoning it,” although essentially the same as “failing to pursue it,” would, in my opinion, also avoid help avoid the implication that you have “failed” to do something.

To abandon your n400 you do nothing. You simply ignore any interview and abandon the application. You can also withdraw the application by sending uscis a letter. It's difficult to tell you how this will affect any future applications without knowing more details about your particular case.

(from Avvo[dot]com: Legal Answers)