If you mean protecting files from user, I think the answer is No, you can't. a user can copy your files simply.
LocalDB always runs under the users security context; that is, LocalDB
never runs with credentials from the local Administrator’s group. This
means that all database files used by a LocalDB instance must be
accessible using the owning user’s Windows account, without
considering membership in the local Administrators group.
For more information see Permissions section in SQL Server 2012 Express LocalDB
I believe you have the option to encrypt and decrypt data using .Net Framework and TSQL methods, but you can't protect your database objects using database encryption options since TDE (Transparent Data Encryption) is not supported by LocalDB.
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