I'm not sure where it fits in the LSJ entry to be honest but ἀξιῶ can mean something like "claim" or maybe even just "think" with accusative and infinitive, e.g.
διὰ ταῦτ’ ἐγὼ τὴν ῥητορικὴν τέχνην ἀξιῶ εἶναι περὶ λόγους (Gorgias 450c
οὐ δὴ ἀλόγως, ἦν δ’ ἐγώ, ἀξιώσομεν αὐτὰ διττά τε καὶ ἕτερα ἀλλήλων εἶναι (Republic 439d
Here, I'm not sure there's all that much difference between άξιώσατε and the οἰήθητε that follows. These examples in fact don't seem to be covered by the LSJ entry at all since it only mentions acc. pers[onal] with "think fit." Perhaps the definition "think, deem" includes the acc. + inf. construction as it's a standard construction for verbs of this meaning?
The Jowett translation
has "I will ask you then to assume with me".