If a creature has both lifelink and deathtouch does one damage to a creature gain you life and kill it?

Absolutely. Both abilities work simultaneously and independently. Deathtouch (CR 702.2) means any amount of damage that source deals to a creature is considered lethal, so even 1 damage is enough to destroy it. Lifelink (CR 702.15) means damage dealt by the source also causes its controller to gain that much life — so dealing 1 damage gains you 1 life.

Importantly, both abilities trigger from the same damage event. You do not need to deal damage equal to the creature's toughness to get the lifelink — any damage dealt counts (CR 702.15b). And deathtouch does not reduce or alter the damage amount, so lifelink still applies to the full damage dealt.

State-based actions then check the damaged creature (CR 704.5g): since it has been dealt damage by a deathtouch source, it is destroyed the next time state-based actions are checked, regardless of its toughness.

Example: You attack with a 1/1 Snake that has both deathtouch and lifelink. Your opponent blocks with a 5/5 Dragon. The Snake deals 1 damage to the Dragon — you gain 1 life from lifelink, and the Dragon is destroyed by deathtouch. The Snake dies too from the Dragon's 5 damage, but both effects still resolved correctly.

This combination is extremely efficient and is why cards like Ochran Assassin or a deathtouch/lifelink Infect creature are considered so powerful in combat.