1. You don't seem to know when you are lucky. ( Context will be shown in the picture below)
I think "know" is used intransitively, with when-clause being adverbial.
Another analysis is that "know" is a transitive verb here, and the when -clause, being a norminal relative clause, functions as its object.
The latter analysis suggests "when" is in the same sense as:
2. Do you remember when we went to Norway? That was a good trip. (LDOCE)
I'm not sure I agree. What do you think?Thank you.

Greetings,
While I find BillJ's analysis plausible, I think there is something to be said for the analysis toward which you are inclined, Robby. Please note that BillJ is not saying the "when"-clause is a "nominal relative clause"; he is saying the "when"-clause is a subordinate interrogative clause, i.e., an embedded question.
I feel that there may have been some miscommunication when you asked whether "know" could alternatively be analyzed as intransitive in "You don't seem to know when you're lucky!" and BillJ then pointed out that "know" is considered intransitive when its complement is an embedded question. 
In your first post, quoted above, your intransitive analysis crucially involved treating the "when"-clause as adverbial. If it is adverbial, it is not the complement of "know." It could actually be fronted, as all adverbial "when"-clauses can: "When you're lucky, you don't seem to know!"
I think that that analysis of the "when"-clause and "know" does make a lot of sense in the context. Of course, "know" has an implied object or complement on this analysis, though it is used intransitively. The sentence may be regarded as equivalent to either sentence below.
- When you're lucky, you don't seem to know it!
- When you're lucky, you don't seem to know that you're lucky!