I use Premature Burial, and revive Sacred Crane with no more cards remaining in my deck. Now, since I have no more cards to draw for Crane's effect, would I lose right there, or would I lose when I can't draw during my draw phase next turn?

No, you wouldn't lose just yet. You can only lose when you can't draw during your draw phase.

Anytime you are forced to draw and there are no cards left in your deck (or not enough to draw), you lose.

It does not matter what phase you are in, if a card forces you to draw and there are no more cards left in the Deck to draw from, you lose.

Isn't Sacred Crane optional though?

Only thing optional about Sacred Crane is NOT summoning it.

If you Special Summon it from the Graveyard (or Special Summon it "period"), you must draw a card. Drawing ANYTIME during your turn from a mandatory effect will force you to lose if you cannot draw the required amount of cards from your Deck.

Yep...Crane is NOT an optional drawing effect.

Just a little sidenote that things like Cyber Jar, Reasoning, Monster Gate, etc would NOT give you a game loss since they do not force you to "Draw", but to "pick up" cards.

Whoops!

My bad...

Just dont pick up a "Sacred Crane"....

That's true...lol...(and no rule saying it has to Special Summoned face-up)

Official rule book version 6.0 under "special summon" (p15) :

Unless otherwise specified, a special summoned monster is summoned onto the field in your choice of face-up Attack position or face-up defense position.

Cyber Jar allows you to place monsters Special Summoned by its effect "face-down".

that would fall under "unless otherwise specified"

I know all Special Summons have to be face-up Attack or Defense Position unless otherwise specified...I said that there were no rules for Sacred Crane saying it has to be Special Summoned face-up for you to draw a card...

but wouldn't it need to be face-up for its effect to trigger?