As Vampiric Scepter a necessary component for almost all of the life steal items (the only exception is Guinsoo's Rageblade), Vampiric Scepter is useful for any stage of the game.
Vampiric Scepter increases the sustain of any champion, but it is best used with auto-attacking champions as lifesteal only works with basic attacks. Ranged champions, such as Ashe or Tristana, are able to restore health while being relatively safe. Melee champions, such as Jax or Wukong, are in more danger to be damaged if an enemy champion is nearby.
Vampiric Scepter is often used with Doran's Blade, allowing champions to stay in lanes for extended periods of time without needing to go back to base to heal. Doran's Blade is often the preferred item as it also adds health, but its drawbacks are not building into other items .