Tomebound Lich

Lifelink is a static ability.

Damage dealt by a source with lifelink causes that source’s controller, or its owner if it has no controller, to gain that much life (in addition to any other results that damage causes). See rule 120.3.

If an object changes zones before an effect causes it to deal damage, its last known information is used to determine whether it had lifelink.

The lifelink rules function no matter what zone an object with lifelink deals damage from.

If multiple sources with lifelink deal damage at the same time, they cause separate life gain events (see rules 119.9–10).

Multiple instances of lifelink on the same object are redundant.

Deathtouch is a static ability.

A creature with toughness greater than 0 that’s been dealt damage by a source with deathtouch since the last time state-based actions were checked is destroyed as a state-based action. See rule 704.

Any nonzero amount of combat damage assigned to a creature by a source with deathtouch is considered to be lethal damage for the purposes of determining if a proposed combat damage assignment is valid, regardless of that creature’s toughness. See rules 510.1c–d.

The deathtouch rules function no matter what zone an object with deathtouch deals damage from.

If an object changes zones before an effect causes it to deal damage, its last known information is used to determine whether it had deathtouch.

Multiple instances of deathtouch on the same object are redundant.