BitLotto runs on the CURRENT chain, but coins are not destroyed but collected. Then the network creates the number for the winner. The winner then gets all the coins.
The problem is that right now, since the winning number is dependent on a secret number, people have to trust BitLotto or any other lotto, to not steal the winnings. For example, if there is a lotto prize of 100 bitcoins, and someone who knows the secret number has 60% of the lotto tickets, then their expected winning is 60 bitcoins. Say this person generates a bitcoin block, worth fifty bitcoins, which is used in combination with the secret number to calculate the winning number. If the winning number would not lead to winning the lotto, the cheater can simply not announce the block to get an extra (60 - 50 = 10) bitcoins. As the bitcoin blocks halve in value every four years, the cheater gets greater winnings. If the lotto prize gets larger, the cheater also gets more winnings. The only way this attack could be guaranteed to be unprofitable is if the lotto prize was smaller or equal to the bitcoin block value.
The lotto operator knows the secret number, also a cracker could break into the system and learn the secret number. Although I believe it unlikely that anyone has gone through the trouble to get lotto winnings in this way so far, as time passes the chance for such a cheat increases, and with this system there is no way for people buying the lotto tickets to know for sure if the random number is being generated fairly.
Making an agreed upon truly random number in a peer to peer system is more difficult than it seems. Some of the issues with making a peer to peer random number are mentioned in the 'Robust Random Number Generation for Peer-to-Peer Systems' paper referenced above:http://www.arnetminer.org/dev.do?m=downloadpdf&url=http://arnetminer.org/pdf/PDFFiles/--g---g-Index1247931776950/Robust%20Random%20Number%20Generation%20for%20Peer-to-Peer%20Systems1247951238765.pdf
There is also the problem that having one entity running a lotto means there is a single target for some kind of legal action.
Isn't it simpler to just make a lottery with the current blockchain?
There's no need of a new one just for this
The problem with making a lottery in the current blockchain is that it would slow development of bitcoin and add potential security holes.
It would slow development because it would increase the complexity of the bitcoin program, which means it would take longer for people to learn bitcoin to the point of being able to contribute. People who want to contribute to bitcoin already have to spend a lot of time to get familiar with the complex program before they can start making any change safely, any additional complexity would make this even worse. Also, if there is a lottery or anything else in the bitcoin program, it slows releases because any change has to be tested against the new lottery code as well as the existing code. Overall, complexity is the main reason why software development slows down as programs gets bigger, and indeed why software development sometimes fails entirely when programs get really big. Bitcoin development is already slowing as the program gets bigger, no function should be added to bitcoin if it could be done in another blockchain.
A script has the same problems as adding the lotto directly to the blockchain. In theory, scripts could add functionality without adding complexity or security holes, in practice they often bring trouble.