लेओगे isn't a valid verb form.
लेंगे is valid and it is used with आप.
आप क्या लेंगे? What will you take/have.
Conjugation of lena (and dena) seem to be an area where there is some variation, either across dialect or because so many people say it "wrong" (i.e. according to one perspective) that another form is accepted. An analogy for what I am thinking is: to say "brang" in English instead of "brought."