Does a court have a duty to instruct on a lesser included offence when the evidence raises a question as to whether all of the elements of the charged offense are present?

A court has the duty to instruct on a lesser included offense when the evidence raises a question as to whether all of the elements of the charged offense are present and there is evidence that would justify a conviction of the lesser offense. (People v. Ledesma (2006) 39 Cal.4th 641, 715.) Here, defendant testified that in the incident on July 14, 2007, he struck the victim once on the head. He acknowledged that the victim's head immediately began to bleed. Although the defense argued that the victim had an existing cut on her head from a swimming accident, it was undisputed that the blow defendant struck caused a cut which necessitated eight staples. Even if the blow reopened an existing, healing cut, the reopened cut is itself a traumatic condition. As to the incident on August 15, 2007, defendant did not deny that he had hit the victim, as

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