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