I've got 2 NPCs in a house I made, their packages work, they go outside as scheduled but one thing still missing is them locking the door to their house. How do make the NPCs do that? I can't find a single tutorial or anything that can help me on this.

I read you have to use Locklists first. I created one, assigned to the cell data, but the two NPCs still aren't locking their doors.

I notice for vanilla NPCs, they all carry keys with them. Do I need to do with same thing and how? Do I lock the doors by default and give my NPCs keys to carry?

From looking at a vanilla Skyrim house, I would say that you need a key. They have their own section under 'Items'. Just create a new one with changing the ID of an existing one (don't overwrite the original ofc), so you get the model and sounds right.

Then at the door reference you have to tick the locked checkbox in the 'Lock' tab. There you can set the lock strength and choose the key, you have created, from a drop-down list.

Oh yeah, as you said, you will have to put the key into the NPCs inventory.

Edit: I guess you have the AI packets set up accordingly? (To lock doors when they go to sleep or leave the house, etc.)