what is the difference between these two phrase?

I heard of:
Lock up your iPad with parental controls.

but can we say
Lock down your iPad with parental controls?

It would be great if anyone can reference me to other good examples.
Generally speaking -

lock up means prevent people from using.
eg The teacher locked up his classroom. More common here is just 'locked'.

eg The teacher locked up the question papers for the next day's exam. He prevented anyone from accessing them

Lock down means to apply strict controls.
eg The teachers locked down the school because the students were in danger. They would not let anyone in or out.
This is not a common expression. I usually hear it only for schools.

In your example, only 'lock down' sounds half-way acceptable. But I'd prefer some other word, like 'secure'.

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Lock up:Other do it .Inmates are locked up in the night by the prison warders.

Lock down:You do it yourself. The authorities demands lock down of your place or the whole vicinity ,to prevent /protect from calamities.

Lockup - Corrective Action

Lockdown - Preventive Action

For more details refer to definitions of Corrective and Preventive actions.

Thank you for the space to comment my views.

I think lock up and lock down are two different phrases used for different contexts or situations.

1. Lock up the culprit.

2. Many countries are locked down seeing the rapid spread of fatal COVID-19 .

Case 1) Lock up is used for putting culprit into the prison to prevent from committing any crime further. Moreover, prison is meant for criminals, offenders or culprits and so, when the task of captivating gets accomplished by putting them there, the phrase 'lock up' is used.

Case 2) Lock down ,here denotes to withholding people or abstaining people in their confinements or houses with a certain objective while putting a hault to all the economic, commercial, industrial or occupational activities. Here, the workers ,or professionals or activity performers get down to their homes.

Now, one can make out from the above mentioned examples

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