is there a rule for which followers are loyal and who are not?

example

when you have lydia

she will assist you even if you hit the Jarl

while others turn on you...how to know?

Each follower has an internal morality statistic, symbolized by a number ranging from 0 to 3. Simply put, 0 is effectively lawless, while 3 is completely lawful. Housecarls and hired mercenaries (for example, Stenvar, Jenassa and Marcurio, etc) have a moral stat of 0. They'll go along with anything you do, and follow illegal orders.

The UESPWiki lists the morality stat for every NPC in a summary sidebar. Look for the phrase "Any crime" - if you see that, you'll know that the follower in question is entirely "loyal," as you put it.