In the book by Lehalle and laruelle - "market microstructure in practice" -
"The trading activity of HFT updates limit orderbooks at a higher rate than the round trip for any non-colocated observer. The snapshot of the limit orderbooks you take into account to make decisions does not, in most cases, reflect the state of the book when your order actually reaches it... when the orderbook update frequency f is larger than two times the traveling time information (i.e. f > 1/(2τ)), the decision-making process does not use the proper information to decide where and how to route an order. "
However, we don't see this being used in any research paper as a threshold for market efficiency estimates. From the point of view of a market practitioner, there should be lower bound at which exchanges have to segment their market data feeds to a higher number - such that these feeds are usable by the participants.