I have a question about the homonculus monster from the Monster Manual. It is said that "A master can have only one homunculus at a time (attempts to create another one always fail), and when its master dies, the homunculus also dies."

So my question is: Could an undead, a lich for exemple, create an homonculus? Scince it's already dead, does it make the homonculus unable to die with it's master, or would the ritual simply fail? 

Lich are not dead.

They are undead.

Yes, any undead with the ability to cast the spell can create an homunculus and when the undead creature dies (goes to being "dead" instead of "undead") the homunculus dies too.

If you wanted to get fun and technical with it, the lich would still have to have blood in it's body to cast the spell initially, so an ancient lich may not be able to summon a homunculus.

Thank you for your answers!