Some schools give you a 2 week deadline and some give you months for returning the Secondary. It's fine to submit the Secondary after being formally invited to do so, regardless of whether the LOR is received yet.
There is no "official" definition of what constitutes an early or late application. I've seen various definitions on SDN. Is knowing you are on the late side going to change anything or just make you worry more?
I'd go by :
June to mid July=Early
Mid July to End of August=Average
(I'll add this one just for you)First week of September=getting toward late.
September to Mid October=Late
>Oct 15=Very late.
What does being late mean? It means that you are statistically less likely to get an interview at a given school because less interview slots remain. If you're an average applicant, this is perhaps 2% less in early September, 5% less by mid September, 20% by the end of September, 60% by midOctober, 95% by early November. The steepness of the curve varies depending on the school and how competitive you are for it. Yes, I'm just pulling these numbers out of my hat based on personal experience/impressions, not because of published data, the intent being illustrative purposes.