Does Liandry torment extend deathfire touch?

Yes, and deathfire touch extends Liandry's torment creating an infinite burn.

In reality, nothing "extends" death fire touch. Single target spells proc deathfire for 4 seconds, Liandries only lasts 3 seconds, so it's not going to make a difference.

edit: The only things that "extend" deathfire touch is DoT abilities that last longer than 4 seconds. So, mordekaisers ult and that's basically it.

it stacks it