To teach New Testament Greek, you need to have a handle on the Greek of the Septuagint.
Housman had some pungent things to say about the (editors of) the Thesaurus Linguae Latinae, but he was not really attacking thesauruses per se. They are pretty useful. Faced with a bold assertion in a text book on the use of such and such a word, you can often check to see if it is true. Unfortunately the Perseus Project does not include the Septuagint and I have not yet worked out how to use the TLG.
Bible Researcher provides two pages of relevant information: one on the Septuagint and the other on Greek versions of scripture. (That looks like afterthoughts in site design rather than a really subtle distinction.)
Septuagint Online : Tools and Resources is a gateway to a mine of information on the Septuagint.
Septuagint.org is an ambitious attempt to have a fully parsed version of the Septuagint. I could do without the parsing and would prefer an index. It seems to have been forgotten and was supposed to have moved to its new home where none of the LXX has yet arrived.
The Apostoliki Diakonia of the Church of Greece presents itself as an official website of the Greek Orthodox Church. I have no idea if this is true. It claims that Ieronimos II Archbishop of Athens) is Chairman. The design, to my eyes, is reminiscent of a certain other *cough* Ecclesiastical website.
Whoever they are they at least have the complete Septuagint.
New Advent has the Septuagint with parallel English (Douay Rheims) and Latin translations.