Sybil attack
I am not sure how the sybil attack would work in this scenario. I would have thought the lottery system would attract a large number of cheap nodes. An attacker would find it difficult to get a useful proportion of nodes into the system to allow them to influence the network. ie PoW requires more hashing power in order to get a useful proportion, whereas here actors would all be increasing their own node count.
I think the sheer number of nodes combined with inherent network latency would mean that forking would be rampant, and there would be insufficient time to identify the best chain and re-sync across the network. The system would simply 'fork' itself to death