Is A Landlord Required To Provide A Mailbox With A Lock On It If It's An Apartment House In The State Of Kansas?

I can't speak for the laws in Kansas, that's something you need to check out, but it would seem that common decency would compel you to put a lock on a mailbox in an apartment building.  The risk of mail being stolen in an apartment building is very high.  I lived in apartments for years, and every place had mailboxes that locked.  With identity theft at an all time high, it's always a good idea to have locked mailboxes when there's more than one tenant living in a building.   

No, If you need mail box then you can only request to your landlord. Or  rent an apartment with mailbox.

The US Post Office has rules for delivery to apartment mailboxes.

Call a local office to see whether the delivery location meets the requirements necessary.