@ryan Good question. I've had a brief look at the paper mentioned. The list representation task from the paper is a "weaker" task than the task in the question, so the lower bound from the paper applies here. However, this does not answer the question, for reason a related to David's first remark.

Theorem 1 in the paper states that at least Omega(log n / loglog n) amortized time per operation is required. The main result that supports this theorem, theorem 3', makes it more clear what this means: there exist a sequence of m operations such that any algorithm takes Omega(m*log n / loglog n) time.

So, while the lower bound does imply that it is impossible to do better than Omega(log n / loglog n) for all operations, the lower bound does not directly apply , because we allow O(log n) for 1 operation. However, log n and log n /loglog n pretty close, so I wouldn't be surprised if the proof of the paper can be adapted to get an Omega(log n) bound under the assumption that the report function takes O(1) time.

Fun fact: the paper writes "This provides a separation in power between a RAM with disjoint bytes and a RAM with byte overlap (RAMBO [12])." and in the references "[12] S. Stallone, First blood, United Artists (1982)."