I've been playing a necromancer lately and I'm also a heavy roleplayer. I'd like to know if a vampiric necromancer would be able to achieve lichdom in elder scrols lore.

Well, perhaps some curse could turn him or her into an undead mage. Which is pretty much a lich.
Like with Draugr, but it is unlikely.

Theoretically, possibly..

Vampires and Liches are already undead. Not sure if the Vampire still retains their soul... if so, your necromancer character can pray to the God of Worms to receive the neccessary instructions on how to go about doing it.

SPecific details on the process for Lichdom can be found http://www.uesp.net/wiki/Oblivion:The_Path_of_Transcendence. It doesn't spell out what the actual process is, but it should grant you a lot of insight into how the process would work.