The option to Lockdown a Persona is made available once you reach Rank 3 in the Strength Confidant (Caroline and Justine). For information on how to reach this, you'll want to refer to Great Phantom Thieves Convene.
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https://psnprofiles.com/guide/5919-persona-5-trophy-guide#28...)
When you Lockdown a Persona, you're not able to use it for a while, but it will earn a skill that it couldn't just from leveling up. This takes a number of in-game days to occur. Caroline will contact you on your mobile phone on the day before the Persona will perish, so make sure you head back to the Velvet Room and take it out. You will earn the trophy upon taking it out of Lockdown when the Persona has learned a new skill.