Yes you can add both the sugar and lemon juice.
In this case, they are strictly for flavor. The lemon juice would simply add MORE acid, increasing safety if anything.

Deanna

Thank you Deanna!
I had read a couple of different places that red mulberries are not as acidic as other berries. The information I found recorded a pH of 4.33 for the Red Mulberry. I know there are variations in pH depending on variety, growing conditions, etc., so I feel better adding the lemon juice. I think it improves the flavor as well. I also wanted to be sure that the 1 to 2 cups of sugar in the recipe weren't necessary, but could be adjusted to preference. So thank you for answering my questions!
Karli