When Wurmcoil Engine dies, it and Luminous Phantom trigger if its on the battlefield.
Resolve the Luminous Phantom trigger, if applicable, causing you to gain 1 life.
Resolve the Wurmcoil Engine trigger, creating two 3/3 Wurm artifact creature tokens.
When the Wurms enter the battlefield, Lunarch Veteran triggers twice if its on the battlefield, causing you to gain 2 life.
Activate Phyrexian Altar twice by sacrificing the Wurm tokens, adding ({B} magic symbol) ({B} magic symbol) .
When the Wurms die, Luminous Phantom triggers twice if it is on the battlefield, causing you to gain 2 life.
Activate Chainer by paying ({B} magic symbol) ({B} magic symbol) ({B} magic symbol) and 3 life, putting Wurmcoil Engine from your graveyard onto the battlefield.
When Wurmcoil Engine enters the battlefield, Lunarch Veteran triggers if its on the battlefield, causing you to gain 1 life.