I did consider Gifting for Vamp, but then I had to Gift for Tutors as well. What I want from my Gifts is acually mana. If they giveyou Mystical Tutor and Vampiric Tutor, only one Tutor will be effective Pre-Yawgs Will.
I think you can use use Volcanic Island to Mystical for Yawg Will during your upkeep. Then you draw Yawg Will. During your main phase you:
Sac Lotus for BBB, storm = 1
Vamp for LED BB, storm = 2
Tap Sol Ring and play Yawg Will B, storm = 3
Tap Underground Sea to play Ancestral Recall. B, storm = 4
You drew LED and two other cards. If your other two cards include any mana source, Chain of Vapor, Rebuild, Tendrils of Agony, Gifts Ungiven, Force of Will+Blue, Merchant Scroll+Blue, or Brainstorm then you win.
With Mana/Chain of Vapor:
Play other mana and tap for 1 B1, storm = 4.
Play Lotus for BLUE. BUUU1, storm = 5
Play LED for black. BBBBUUU1, storm = 6
Mystical for nothing, BBBBUU1 storm = 7
Vamp for nothing BBBUU1, storm = 8.
Demonic for Tendrils BBUU, storm = 9.
Tendrils for the win.
If you draw Tendrils you can Demonic for Mana Crypt.
If you draw Brainstorm then you can Vamp for Mana Crypt, Brainstorm into Mana Crypt and win that way.
If you draw into Rebuild then you have to play a game with the Stack where you play LED and then Cycle Rebuild. With Rebuild's Cycle on the stack you crack LED. Once LED resolves you Vamp for Mana Crypt and you win from there.
If you draw Gifts you can Gifts for 4 Moxen. Then you play two Moxen. You are down 2 mana but there is no need to Vamp and Mystical for nothing.
If you draw Force of Will and a Blue card then you can play Black Lotus and crack for blue. Then play LED, Force LED by pitching the blue card and then Drain Force.
On your second main phase crack LED for black giving you BBB5 which is enough to Demonic for Tendrils.
If you draw Scroll and a Blue card then you can actually play Black Lotus with b floating. Crack Lotus for U floating BUUU. Scroll for Force of Will, UU. Then play LED, Forcing LED and Draining Force. Again you get BBB5 on second main phase and win.
Anyway depending on your exact list this split has a very high chance of winning. I would guess it is well over 90%. You could be super unlucky and get double Mana Drain
Note that if Force is in your graveyard (and it might have been in mine) then the only two cards you can draw and not win with are if you get really unlucky and topdeck DSC and Recoup.