What does Ordo Templi Orientis really mean? According to Grand Lodge, it means "the Order of Oriental Templars" or "Order of the Temple of the East." Let's explore the actual definitions of the latin...
[a series, line, row, order];
military [a line, rank, file];
politically and socially, [an order, rank, class];
in general [order, arrangement];
templum -i n.
[a section, a part cut off; A space marked off for observation of omens; consecrated ground, esp. a sanctuary, asylum; a place dedicated to a deity, a shrine, temple; any open space, quarter, region; a rafter, crossbeam].
oriens is a form of orior oriri ortus
[to rise; to spring up , be born, proceed from a source or cause].
Hence participle: oriens -entis, [rising].
M. as substantive [the rising sun; the East; the Morning].
(Eastern = orientalis adj.)
Orior as a verb can also mean: rise, arise; spring from, appear; be descended; begin, proceed, originate.
Ordo Templi Orientis
This grouping of words, based on the latin above, can therefore also mean:
Order of the Temple of the Rising Sun Order of the Temple of the Morning
or even The Order of the Rising Temple
I fully admit that I am not an expert in Latin. If you can see any errors in my findings, please let me know.