PMSL @ you all! Funny way to start the day.
silver It takes 3-10 days for the cord to break away. One point of a lotus birth is that it pretty much forces the mother to stay in bed with the baby for a week which is a really good thing (take it from me who was doing stuff WAAY too early, for various reasons). Having looked into it a lot more, there are other reasons people do this, and a lot of it seems to be to do with allowing things to happen naturally rather than artificially ripping the baby away from the security he's always known, and there is anecdotal evidence to say that lotus babies are calmer and more able to cope with the transition from womb to world. However I'd say that this is likely to be because the mother is with the baby for the whole time, there's likely to be plenty of skin to skin and breastfeeding and so on.
The important thing to me is the physiology of allowing all of the cord blood to drain back into the baby before it's cut. It may take 10 minutes - it may take longer - it won't really matter as you'll be delivering the placenta anyway and involved in other things so don't worry about the difference between 10 minutes and an hour. In the hospital though you just may not have so much relaxing leeway as they tend to want to clear the labour room ASAP.
Regarding Vitamin K. It's been shown to dramatically reduce the chance of the baby having a serious but rare condition called Hemorrhagic Disease of the Newborn. On the cons side, there was some evidence which appeared to show that babies given VitK at birth had a higher chance of contracting Childhood Leukemia. Over the past 6 years since I had LC the evidence has come on a lot. My understanding (but check this) is that there are two options for giving VitK - 1) by injection and 2) by mouth. The second option needs about 3 doses over some weeks (not sure how many) but is much less traumatic for baby AND parents (trust me ) and also apparently doesn't have any link to Leukemia.
On the other hand, the recent evidence also seems to show that the injection-leuk link is extremely tentative as well and the benefits of avoiding the Hemorrhagic disease are significantly higher. I don't know the actual statistics.
There's an NCT sheet explaining the up to date information, and your MW will know of course.
FWIW I didn't let LC have the Vit K at birth at all, but will be going for the VitK by mouth this time.
Hope this helps.