For example, if you draft Lurking Automaton as the third card in a draft round and then another one as the sixth card in a draft round, each Lurking Automaton that enters the battlefield under your control does so with six +1/+1 counters on it.

If a Lurking Automaton owned by another player enters the battlefield under your control, the number of counters it enters with will be based on the highest number you noted as you drafted a card named Lurking Automaton, not as its owner did. Unless you also drafted Lurking Automaton, this will be considered 0.