Louw and Nida’s Greek-English Lexicon of the New Testament: Based on Semantic Domains lists τηρέω in more than one semantic domain, one of which groups it with φυλάσσω (section 36.19) and explains the meaning as “to continue to obey orders or commandments — ‘to obey, to keep commandments, obedience.’”
The more I read Greek from the same period as the New Testament, the more I doubt that τηρέω actually had that meaning as a real possibility. LEH (Septuagint lexicon) does not list “obey” as a possible meaning of τηρέω. I don’t have access right now to BDAG, so I can’t check that one. What leads me to the conclusion that Louw and Nida have made a faulty connection here, though, is not other lexica. It is the contexts in which I find this word outside the New Testament.
The fields of meaning for τηρέω center around notions of maintaining, safeguarding, caring for… not right and wrong conduct. Τηρέω is in an important sense an opposite of λείπω (leave, abandon, forsake).
Take John 14:21, for example.
ὁ ἔχων τὰς ἐντολάς μου καὶ τηρῶν αὐτὰς ἐκεῖνός ἐστιν ὁ ἀγαπῶν με
The sense here is probably, “The one who has my commandments and does not abandon them is the one who loves me.” Keeping the commandments in this sense implies remembering them, being aware of them, not forgetting or ignoring them, etc. While this clearly implies following the commandments, the emphasis is not on obedience—something that can be forced—but on willing faithfulness.
This may seem like a minor distinction, but I think it is an important one. There were other ways to talk about “obedience,” the kind of thing a servant does in relationship to a master, and this was clearly an accepted model for talking about the relationship between a person and God in early Christianity. Paul referred to himself as a δοῦλος Χρισττοῦ Ἰησοῦ (Rom. 1:1, Gal. 1:10), for example.
I am not arguing that this is a foreign image to early Christianity, but that the word τηρέω was not used for this purpose. When τηρέω was used in relation to commandments, the emphasis was on remembering them, being aware of them, safeguarding them, etc. It is a positive image, not one of dominance.