One Rule, Four Book Examples

Diptote Causes — Foreign Origin and Its Conditions

إِبْرَاهِيم: foreign proper name, more than three letters—diptote.
شَتَر: the book’s foreign proper name, three letters with a vowelled middle—diptote.
لِجَام: not originally a proper name—fully declinable.
نُوح: three letters with a sākin middle—fully declinable.

Method: check original proper-name status, then length, then the middle letter of a three-letter name.