I tend to agree that your graph does look like the unbuffered one
Sometimes the scale of the graph can be changed and the graph looks different, or you could try taking smaller volume readings around the buffer zone. I am really not sure about your data.
Other possibilities are that lysine is not a good buffer.
Maybe you could try it with a more dilute NaOH solution.
I'm sorry I don't know much more to explain your graph.
Did you put the buffer solution in? Did other people do the same experiment and get the same results?