Having a lottery is a good idea and one I support for grants in general. The grant review process should be simply "is this idea viable and worthy of funding - yes or no”. If yes put it into the lottery and fund as many good grants as you have resources. Peer review works well for this type of sorting, but it is terrible for trying to pick a top 10% idea from a top 15% idea. It just isn’t possible for even the best scientists to be able to do this consistently.

The problem with fellowships is that the longest I know of only go for 5 years and most of the junior ones are only for 3 years. This is just not long enough to take the chance on failure.

If you want to encourage young talented people to tackle really hard and high risk problems you need to provide funding for at least 10 years.

I would go as far as adding a restriction that recipients of these high risk fellowships can’t publish in anything but the absolutely top tier journals (Nature, Science, Cell, etc) for the first 7 years so they don’t get distracted from the high risk work that other scientists can’t afford to do.