The Calm Before The Storm
Judging from this scenario, we can come up with many reasons. It could be that the lioness had much experience with her cubs, and seeing the baby deer stimulated her maternal instincts. It could also be that she was a good-natured lion who preferred peace.
The worse option is that maybe she was calming the waves first and was waiting for the right time to attack, kill, and devour the poor animal. Either of the three, we cannot deny that she cared for the deer even in the short period they encountered one another. While that can be surprising, what the photographer saw next left him stunned.