No drinking lemon juice does not kill off sperm.
If lemon juice killed off sperm when you drink the lemon juice then there would be a lot less babies being born.
Many guys drink lemon juice including my husband especially during the summer months and he still had good sperm and made us some kids.
There's no way for the sperm to be killed by lemon juice or any other food or drinks.
I've heard that eating bacon can kill sperm as well but that's not true either.
My husband loves his bacon too and his sperm was just fine.
Some guys have less fertile sperm though but it's not because of the lemon juice, bacon or any other foods or drinks you consume.