Hello ivicacevis,
Welcome to the forum.
Is it possible to achieve that, ...
In programming, nothing is impossible.
You mentioned portable and cross platform, but you should know they are not the same. Portable (application), cross platform and cross compile are actually 3 different things.
Lazarus can create portable applications. Yes, (almost) all the programs I created are portable, they require no install. They auto generate necessary setting and config files on their first run.
Lazarus is cross platform, you can use it on Linux, Windows and Mac. Lazarus also is cross compile, I can generate Windows binaries when using Lazarus on Linux.
About the database, Lazarus supports wide range of databases. Just pick the one that suits your need: Advantage, DBase, TurboPower FlashFiler, in memory, Firebird, (Visual) FoxPro, Interbase, Ms. SQL Server, MySQL, ODBC, Oracle, Paradox, PostgreSQL, Sybase, SQLite, text files.
Source:
http://wiki.freepascal.org/DatabasesAbout the security and privileges (change, save, lock, etc), it's all depends on the programmer skills and/or the database you choose.
... distribute to end-user via email as zipped file? I never tried, but it sounds very possible to me. You just need to write an import/export module to handle it. Lazarus has ready to use data/file compression modules.
What steps should I take?
Wow, it's a long journey. I'll let more experienced seniors to answer.