If someone is electrocuted, do they have to die or can they just be injured?

Is it correct to say I electrocuted my friend if he was only injured by electricity?

The term electrocute was originally coined in 1889¹ by splicing the prefix electro- into the word execute. It originally meant execute (by electric shock). However, its meaning has evolved over time: first to also include accidental death by electric shock and later to include electrical injury,² generally serious in nature. So your use of the word does not fit the original nineteenth century meaning, but is perfectly in line with the broader meaning of the word as it is understood today.

Oxford Dictionaries says:

electrocute: injure or kill (someone) by electric shock.

So, yes, if someone is electrocuted, they can just be injured.

My husband is an electrician. He reports that in the industry, electrocute is always used to mean death by electricity. They say electrified or (colloquially) lifted to mean receiving an electric shock that is not fatal.

You will sometimes see people use it incorrectly when they actually mean shock or, in other words, when someone or something receives an electrical current.

Electrocution actually derives from electricity + execute: “to put to death by means of electricity”. So the correct usage means that someone or something has been killed via powerful electrical current.

Also I may mention that an electrocution also implies the intent of death. So you may electrocute your friend if the intended outcome is their demise, though they may live through it.