Reaction of cyclohexene oxide with LDA
Because of the steric hindrance of the two iPr groups, LDA is a very poor nucleophile. It is, as you note, a very strong base. The two products observed both arise from deprotonation of cyclohexene oxide.
Deprotonation of one of the methylenes alpha to the epoxide ring opens it to give the allylic alcohol.
Removal of one of the protons on the epoxide ring carbons opens the ring to the enol, which on quench gives cyclohexanone.